Question

Let A = [1 2; 8 18], b1 = [-2; -10], b2 = [2; 8], b3 = [2; 14], and b4 = [4; 22]. a. Find A^-1 and use it solve the four equations Ax = b1, Ax = b2, Ax = b3, and Ax = b4. b. The four equations in part (a) can be solved by the same set of operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix [A b1 b2 b3 b4]. a. Find A^-1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The inverse matrix is A^-1 = [ ]. (Type an integer or simplified fraction for each matrix element.) B. The matrix is not invertible.

          Let A = [1 2; 8 18], b1 = [-2; -10], b2 = [2; 8], b3 = [2; 14], and b4 = [4; 22].
a. Find A^-1 and use it solve the four equations Ax = b1, Ax = b2, Ax = b3, and Ax = b4.
b. The four equations in part (a) can be solved by the same set of operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix [A b1 b2 b3 b4].
a. Find A^-1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
A. The inverse matrix is A^-1 = [ ]. (Type an integer or simplified fraction for each matrix element.)
B. The matrix is not invertible.

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$Let A = [1 2; 8 18], b1 = [-2; -10], b2 = [2; 8], b3 = [2; 14], and b4 = [4; 22]. a. Find A^-1 and use it solve the four equations Ax = b1, Ax = b2, Ax = b3, and Ax = b4. b. The four equations in part (a) can be solved by the same set of operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix [A b1 b2 b3 b4]. a. Find A^-1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The inverse matrix is A^-1 = [ ]. (Type an integer or simplified fraction for each matrix element.) B. The matrix is not invertible.$

Added by Wesley E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Joel Mueller

06/20/2022

Step 1

Step 1: Write the augmented matrix [A | b] for each equation: \[ A = \begin{bmatrix} 9 & 2 & 1 \\ 4 & -8 & 1 \\ 2 & 1 & 0 \end{bmatrix} \] \[ b_1 = \begin{bmatrix} 2 \\ -2 \\ -10 \end{bmatrix} \] \[ b_2 = \begin{bmatrix} 18 \\ 14 \\ 4 \end{bmatrix} \] \[ b_3 = Show more…

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Let A = and b4 Find and use solve the four equations Ax = b, Ax = bz, Ax = b3, and Ax = b4. The four equations in part (a) can be solved by the same set of operations, since the coefficient matrix is the same. Solve the four equations in part (a) by row reducing the augmented matrix [A b, bz b3 bal]. Find Select the correct choice below and necessary; fill in the answer box to complete your choice. 0A The inverse matrix is (Type an integer or simplified fraction for each matrix element). The matrix is not invertible.

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Transcript

00:01 Okay, so to do this, we need to find the inverse matrix of a.

00:05 So i'm going to write a.

00:06 I'm going to write an augmented matrix that on the right side has the identity matrix.

00:13 Now i'm going to get this into row reduced echelon form.

00:16 So i'm going to multiply row two, and i'm going to add it to negative 8, row one, and that's going to become the new row two.

00:28 So i get 1, 2, 1 ,0.

00:34 Negative 8 times 2 is negative 16 plus 18 is 2 and then negative 8 times 1 is negative 8 plus 0 is negative 8 so now here's what we have i'm going to multiply 1 half row 2 and that's going to become the new row 2 so i get 1 0 2 2 1 negative 4 1 1 1 half 0 and then i'm going to take negative row 1 or excuse me negative row 2 negative twice row 2 how about i need to cancel that 2 so i need to take negative twice row 2 and add it to row 1 and that's going to become the new row 1 so i get 0 1 1 here 0 here negative 2 times negative 4 is positive 8 plus 1 is 9 and then negative 2 times 1 half is negative 1 plus 0 is negative 1.

01:52 So here is what we have.

01:55 So my a inverse, my inverse matrix is 9, negative 4, negative 1, 1 1⁄2 .5.

02:02 To see that if we did it correctly, let's take 1 ,8, 2, 18, and multiply it by the inverse.

02:11 So we get 1 times 9 is 9 plus 2 times negative 4 is negative 8, 9 plus negative 8 is 1.

02:25 8 times 9 plus negative 8 is 72...

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