Find the inverse of the following matrix. Write entries as integers or fractions in lowest terms. If the matrix is not invertible, type "N" for all entries. -5-1021 A = -2-5 9 1 2 -4
Answers
The inverse of matrix A is given by;
A^-1 = |5/139 -189/139 29/139 |
|-10/139 129/139 -27/139 |
|-5/139 19/139 -3/139 |
The given matrix is A =
| -5 -10 21 |
| -2 -5 9 |
| 1 2 -4 |
To find the inverse of a matrix, first find the determinant of that matrix. The determinant of matrix A is given as;
|A| = -5(-5(-4) - 2(9)) - (-10)(-2(-4) - 1(21)) + (21)(-2(2) - 1(-5))
|A| = -5(10) + 100 - 21(9)
|A| = -50 + 100 - 189
|A| = -139
Thus, the determinant of matrix A is -139. Now, we can use the formula of inverse of a 3x3 matrix;
A^-1 = 1/|A| * |(b22b33 - b23b32) (b13b32 - b12b33) (b12b23 - b13b22)|
| (b23b31 - b21b33) (b11b33 - b13b31) (b13b21 - b11b23)|
| (b21b32 - b22b31) (b12b31 - b11b32) (b11b22 - b12b21)|
where b is the cofactor of each element of matrix A.
The cofactor of element aij is denoted as Aij and given as Aij = (-1)i+j|Mij|.
Thus, the cofactors of matrix A are;
|-5 -10 21|
| -2 -5 9 |
| 1 2 -4 |
M11 = | -5 9 |
| 2 -4 |
M12 = | -2 9 |
| 2 -5 |
M13 = | -2 -5 |
M21 = | -10 21 |
| 2 -9 |
M22 = | -5 -21 |
| -2 5 |
M23 = | -2 -2 |
M31 = | -10 -5 |
| 2 9 |
M32 = | -5 -9 |
| 2 2 |
M33 = | -2 -2 |
Now we can find the inverse of matrix A as follows;
A^-1 = 1/-139 * |(5 189 -29)|
|(-10 -129 27)|
|(-5 19 -3) |
Hence, the inverse of matrix A is given by;
A^-1 = |5/139 -189/139 29/139 |
|-10/139 129/139 -27/139 |
|-5/139 19/139 -3/139 |
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Related Questions
The figure below shows the letter Z and four of its transformed images-A, B, C, and D: A coordinate plane is shown. The letter Z has endpoints at negative 6 comma 3, negative 6 comma 1, negative 4 comma 1 and negative 4 comma 3 and has a diagonal line that goes from top right to bottom left in between. A is a shape that has endpoints at 4 comma 3, 4 comma 1, 6 comma 3 and 6 comma 1 and has a diagonal line that goes from top left to bottom right. B has endpoints at negative 6 comma negative 1, negative 6 comma negative 3, negative 4 comma negative 1 and negative 4 comma negative 3 and has a diagonal line that goes from top right to bottom left. C has endpoints at negative 3 comma negative 1, negative 3 comma negative 3, negative 1 comma negative 1, negative 1 comma negative 3, and has endpoints that go from top left to bottom right. D has endpoints at 2 comma negative 1, 2 comma negative 3, 4 comma negative 1, and 4 comma negative 3 and has a diagonal that goes from top right to bottom left. Which of the four images was formed by a reflection of the letter Z? (5 points) A B C D
Answers
Answer:its c
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
The answer is A because a reflection would be Reflected so its on the right side of the graph and the Z is facing the other way as if it were a literal reflection which it is.
Hope my awkward way of explaining this helps you on your test since i just passed mine and it said A was correct.
Graph g(x)=5|x -6|+2g(x)=5∣x−6∣+2g, left parenthesis, x, right parenthesis, equals, 5, vertical bar, x, minus, 6, vertical bar, plus, 2.
Answers
The graph of the absolute value function can be seen at the end of the answer. There we see a translated and dilated parent function.
How to graph the absolute value function?Here we want to graph:
g(x) = 5*|x - 6| + 2
First, remember that the minimum of the absolute value part |f(x)| is 0, so the minimum of the above function is 2, and that happens when x = 6. That will be the vertex of our function.
From that point, we will have two lines, one that goes to the right with a slope of 5, and the other that goes to the left with slope of -5 (the coefficient that multiplies the absolute value part of the function).
The graph of the function can be seen below.
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Answer:6,2 & 7,7
Step-by-step explanation:
Integral from 0 to x 2sec^2(2t+pi/4) dt
Answers
The integral of the function is A = tan ( 2x + π/4 ) - 1
Given data ,
Let the function be represented as F
Now , the value of F is
F = ∫₀ˣ 2 sec² ( 2t + π/4 ) dt
On simplifying the integral , we get
A = 2 ∫₀ˣ sec² ( 2t + π/4 ) dt
On applying u-substitution , we get
A = 2 ∫ ( π/4 ) to ( 2x+π/4) sec² ( u ) du
Now , A = 2 ( 1/2 ) [ tan u ] ( π/4 ) to ( 2x+π/4)
On further simplification , we get
A = tan ( 2x + π/4 ) - 1
Hence , the integral is A = tan ( 2x + π/4 ) - 1
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- The zoom feature on a camera lens allows you dilate what appears on the display. When you change from
100% to 700%, the new image on your screen is an enlargement of the previous image with a scale factor of
7. If the new image is 70 millimeters wide, what was the width of the previous image?
a. 245 millimeters
35 millimeters
b. 490 millimeters
d. 10 millimeters
c.
Answers
Answer:
d. 10 milimeters
Step-by-step explanation:
Answer:
10 milimeters
Step-by-step explanation:
100/700 = x/70
x = 10
the eccentricity of the ellipse is approximately Choose... : 0.57, 0.87, 1.15 . This value indicates that the ellipse is more Choose... : circular then elongated, elongated then circular.
Answers
Solution
- The eccentricity of an ellipse is given below:
\(\begin{gathered} Given\text{ the ellipse:} \\ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\ \\ \text{ The eccentricity is:} \\ e=\sqrt{1-\frac{b^2}{a^2}} \\ \\ \text{ From the equation given,} \\ a^2=49,b^2=12 \\ \\ e=\sqrt{1-\frac{12}{49}} \\ \\ e=0.868966...\approx0.87 \end{gathered}\)- The eccentricity is 0.87
- Because the eccentricity is close to 1, it means it is flatter than normal. Thus, it is "elongated then circular"
Final Answer
- The eccentricity is 0.87
- "elongated then circular"
How do I find the roots of a cubic equation?
Answers
Answer:First, we need to find which number when substituted into the equation will give the answer zero. Therefore is a factor. Factorise the quadratic until the expression is factorised fully. Therefore the roots occur when = -3, -2 and 1.
Step-by-step explanation:
Answer:
by reducing it into a quadratic equation and then solving
Step-by-step explanation:
Choose an expression that is equivalent to (-2)^4/(-2)^2. out of these
Answers
The expression that is equivalent to (-2)^4/(-2)^2 is (-2)^6/(-2)^4
How to determine the expression that is equivalent to (-2)^4/(-2)^2?The expression is given as:
(-2)^4/(-2)^2
Apply the law of indices
(-2)^4/(-2)^2 = (-2)^(4 -2)
4 - 2 has the same value as 6 - 4
So, we have:
(-2)^4/(-2)^2 = (-2)^(6-4)
Apply the law of indices
(-2)^4/(-2)^2 = (-2)^6/(-2)^4
Hence, the expression that is equivalent to (-2)^4/(-2)^2 is (-2)^6/(-2)^4
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Exercise 1
Let X = (0,1,2,3,4,5). Complete the following table using the definition of
X-Y
Assign each xin X to the expression 2
1
2
3
4
0
+
What are (0) (0) (0) () and (5)
What the range of
Answers
The range of a set of values is the difference between the maximum and minimum values in the set, the range is 3 - (-2) = 5.
The expression "X - Y" subtracts the value of Y from each value in the set X. If Y is assigned the value 2, then for each x in X, we have:
X - Y = x - 2
the calculation of X - Y for each value in the set X = (0, 1, 2, 3, 4, 5) with
Y = 2
So, if X = (0,1,2,3,4,5), then:
(0) - 2 = -2
(1) - 2 = -1
(2) - 2 = 0
(3) - 2 = 1
(4) - 2 = 2
(5) - 2 = 3
So, the resulting set is (-2, -1, 0, 1, 2, 3).
The resulting set is (-2, -1, 0, 1, 2, 3) and the range is 5.
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From your home, the route to the school that passes the mall is 2 miles shorter than the route to the school that passes the theater. What is the distance to the mall?
Answers
Answer:
4 milles
Step-by-step explanation:
The distance of the mall from the home will be 2 miles.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
\(y-y_{1}=m\left(x-x_{1}\right)\)
We have the following problem -
From your home, the route to the school that passes the mall is 2 miles shorter than the route to the school that passes the theater.
Assume that the route to the school that passes the mall is [x] miles and
the route to the school that passes the theater is [y] miles. Then, we can write the equation as -
x = y - 2
y = x + 2
Plot the graph. The y - intercept will be the distance to the mall which is 2 miles.
Therefore, the distance of the mall from the home will be 2 miles.
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chegg find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x)
Answers
The derivative and domain of the function f(x) = x²-2x³ is :\((-\infty, \infty)\).
What is derivative of the function (differentiation)?The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.
Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.
Calculation for the derivative:
Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).
\(\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}\)
\(\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}\)
\(=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}\)
Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.
\(\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}\)
f and f' are polynomials, so their domains are all real numbers.
Therefore, for f(x) = x²-2x³ domain of f and f' :\((-\infty, \infty)\).
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The complete question is -
Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.
Solve the area of a rectangle formula for the width of the rectangle. A = LW
W= L/A
W = A + L
W = A/L
W = A – L
Answers
Take the original A=LW and divide both sides by L to get A/L=LW/L, the Ls on the right cancel out to leave A/L=W
It’s the reverse operation:)
How would I set this to 0?
Answers
Answer:
− 2 sin ( 0 ) ⋅ sin ( 0 ⋅ π /0 m ) + cos ( 0 ) ⋅ cos ( 0 ⋅ π /0 m ) = 0 is not an identity
Step-by-step explanation:
Francis graphs the system of equations to determine its solution.
3x+2y=12
3x−y=3
What is the correct solution?
Enter your answer by filling in the boxes.
Answers
Answer:
Step-by-step explanation:
3x+2y=12 x= −2/ 3 y+4
3x-y=3 x= 1 /3 y+1
i hope this helps in anyway :/
The solution of the system of linear equations 3x + 2y = 12 and 3x − y = 3 is (x = 2, y = 3)
What is a Linear Equation?If it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Given that the system of linear equations;
3x + 2y = 12 and 3x − y = 3 is
Solving the equations by elimination, we get
x = 2 and y = 3
Hence, The solution of the system of linear equations 3x + 2y = 12 and 3x − y = 3 is (x = 2, y = 3)
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A ball is launched from a 69.92-foot tall platform. The equation for
the ball's height h at time t seconds after launch is h (t) = -16t2 +
6.4t+69.92, where h is in feet. When does the object strike the
ground?
Answers
f(x) = x2. What is g(x)?
Answers
Answer:
B
Step-by-step explanation:
Graph shrinks, that means for every x value there is a higher y value. So coefficient of x is definitely more than 1. Try to substitute x = 1 to (9x)^2 and (3x)^2.
(3(1))^2 = 9
Determine which product has the lower unit price a 16- ounce bag of chocolate for $1.99 or B an 18- ounce bag of chocolates for $2.29
Answers
Step-by-step explanation:
Just divide 16 and 1.99 and 18 and 2.29 and choose the one with less value
I want to estimate the population of dolphins in Ingall Bay. I capture and tag 20 dolphins before releasing them. I then capture 56 dolphins and 7 have tags. Estimate how many dolphins are in the bay.
Answers
It based on this estimation method, the population of dolphins in Ingall Bay is estimated to be around 160.To estimate the population of dolphins in Ingall Bay, we can use the mark and recapture method.
The idea behind this method is that the proportion of tagged dolphins in a second sample reflects the proportion of tagged dolphins in the overall population.
Let's denote the total population of dolphins as P. We can set up a proportion based on the number of tagged dolphins:
Tagged dolphins / Total second sample = Tagged dolphins in population / Total population
Given that 7 dolphins out of 56 in the second sample have tags, and we tagged 20 dolphins initially, we can set up the proportion as:
7 / 56 = 20 / P
Now, we can solve for P by cross-multiplying and then dividing:
7P = 20 * 56
7P = 1120
P = 1120 / 7
P = 160.
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a rectangle has a length of x3y4 inches and a width of xy7 inches . Which expression represents the ratio of the length of the rectangle to do width of the rectangle? (NEED HELP ASAP)
Answers
Answer:
A. x²/y³
Step-by-step explanation:
Given the following data;
Length = x³y⁴
Width = \( xy^{7}\)
Ratio = length/width
\( Ratio = \frac{x^{3}y^{4}}{xy{^7}}\)
Simplifying the equation by applying the law of indices (division), we have;
\(\frac{x^{3}}{x} = x^{3} - x^{1} = x^{3-1} = x^{2} \)
\(\frac{y^{4}}{y^{7}} = y^{4} - y^{7} = y^{4-7} = y^{-3} \)
Hence, rearranging the above values;
\( Ratio = \frac{x^{2}}{y^{3}}\)
Therefore, the expression that represents the ratio of the length of the rectangle to the width of the rectangle is A. x²/y³.
helppppppppppppp pls 15 = 2 + 4 - d
Answers
Answer:
d=-9
Step-by-step explanation:
Answer:
15=6-d
-d=15+6=9
d=-9
Step-by-step explanation:
Derek has already taken 7 pictures at home, and he expects to take 1 picture during every
day of vacation. How many days will Derek have to spend on vacation before he will have
taken 18 pictures?
Answers
Solve this question
Answers
You have to do Cross multiplication,
2x+5 = 1(x+4) which is simply 2x+5=x+4.
1. x+5=4
2. x=-1
Answer:
X= -1
Step-by-step explanation:
2x+5=1(x+4)
2x+5=1x+4
2x-1x=-5+4
x=-1
The number of students at the start of the week that had a late library book was 200 students. By the end of the week there were only 80 students with a late library book? Is it a increase or decrease in by what percentage? 
Answers
On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is 500
obtained is 400
so, percentage - 400/500 X 100 = 80%
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Mrs. Gomez purchased a pair of sneakers for $32.50 and two shirts for
$13.00 each. If Mrs. Gomez pays 8% in sales tax, then what is the total
cost Mrs. Gomez will pay for the sneakers and shirts? *
Your answer
Answers
Answer:
62.86
Step-by-step explanation:
Add the cost of things without sales tax:
32.5+ (13×2)=58.5
Convert percent to decimal:
8/100=0.08
Multiply cost without sales tax by sales tax to get the amount added to the cost:
0.08×58.2=4.656
Add cost and sales tax amount to get total payment:
4.656+58.5=62.856
Round the total payment to the nearest hundredth place:
62.86
please help mee (image included)
Answers
Answer:
B
Step-by-step explanation:
It seems more reasonable
What is the slope of the line that passes through the points
(11, -8), and (6, -1).
Answers
\((\stackrel{x_1}{11}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{11}}} \implies \cfrac{-1 +8}{-5} \implies \cfrac{ 7 }{ -5 } \implies - \cfrac{7 }{ 5 }\)
Nina hired a car in Italy.
The cost of hiring the car was 440 euro.
The exchange rate is 1 euro = £0.8.
Work out the cost of hiring the car in pounds.
Answers
"the sum of a number and 4.”
Answers
assuming the number is unknown we can just say the number is x. sum is addition so x + 4
You may need to use the appropriate appendix table or technology to answer this question.
A population has a mean of 800 and a standard deviation of 200. Suppose a sample of size 400 is selected and
x
is used to estimate μ. (Round your answers to four decimal places.)
(a)____
What is the probability that the sample mean will be within ±5 of the population mean?
(b)___
What is the probability that the sample mean will be within ±10 of the population mean?
Answers
a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.
(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.
The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
= 200 / √400
= 200 / 20
= 10
To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:
For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.
For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.
We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.
(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).
The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.
Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).
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question r5 sketch a graph of y = f(x) that satisfies the following requirements on the interval 0 <= x <= 10.
Answers
To sketch a graph of y = f(x) that satisfies the given requirements on the interval 0 <= x <= 10, we need to have more information about the specific requirements of the function. However, we can make some general suggestions for how to approach the problem.
First, we should determine the type of function we are dealing with. Is it linear, quadratic, exponential, trigonometric, or some other type of function? This will affect the shape of the graph and give us an idea of how to start plotting the points.
Next, we should consider any specific points or features that we need to include in the graph. For example, if the function needs to pass through a certain point or have a certain slope, we can use this information to determine additional points on the graph.
Finally, we should make sure that the graph satisfies the given interval of 0 <= x <= 10. This means that the graph should not extend beyond this range, and any points outside of this interval should be excluded.
Overall, to sketch a graph of y = f(x) that satisfies the given requirements on the interval 0 <= x <= 10, we need to carefully consider the function type and any specific requirements, plot the points accordingly, and make sure the graph is within the given interval.
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answer plzzzzzzzzzzzzzzz
Answers
Answer:
25
Step-by-step explanation:
They are relevant
3x=75
x=75/3
x=25