Question

(1 point) (a) Find the inverse of the matrix $A = \begin{bmatrix} 2 & 6 & -3 \\ 5 & 14 & -10 \\ 1 & 3 & -2 \end{bmatrix}$ $A^{-1} = \begin{bmatrix} \\ \\ \\ \end{bmatrix}$ (b) Use the answer from part (a) to solve the linear system $\begin{cases} 2x_1 + 6x_2 - 3x_3 = -4 \\ 5x_1 + 14x_2 - 10x_3 = 3 \\ x_1 + 3x_2 - 2x_3 = 2 \end{cases}$ $\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} \\ \\ \end{bmatrix}$

          (1 point) (a) Find the inverse of the matrix
$A = \begin{bmatrix} 2 & 6 & -3 \\ 5 & 14 & -10 \\ 1 & 3 & -2 \end{bmatrix}$
$A^{-1} = \begin{bmatrix} \\ \\ \\ \end{bmatrix}$
(b) Use the answer from part (a) to solve the linear system
$\begin{cases} 2x_1 + 6x_2 - 3x_3 = -4 \\ 5x_1 + 14x_2 - 10x_3 = 3 \\ x_1 + 3x_2 - 2x_3 = 2 \end{cases}$
$\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} \\ \\ \end{bmatrix}$

(1 point) (a) Find the inverse of the matrix
A =
< b m a t r i x >
A^-1 =
< b m a t r i x >
(b) Use the answer from part (a) to solve the linear system
2x1 + 6x2 - 3x3 = -4
5x1 + 14x2 - 10x3 = 3
x1 + 3x2 - 2x3 = 2
< b m a t r i x >
=
< b m a t r i x >

Added by Beverly S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Mirza Aslam Beig

Step 1

To find the inverse of a matrix, we can use the formula: A^(-1) = (1/det(A)) * adj(A) where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A. To find the determinant of matrix A, we can use the formula: det(A) = a(ei - fh) - b(di - Show more…

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Find the inverse of the matrix: 2 6 3 5 14 -10 1 3 2 (b) Use the answer from part (a) to solve the linear system: 2x1 + 6x2 = 5x1 + 14x2 + 3x2 3x3 = 10x3 + 2x3 3 2 x1 x2 x3