(3) Find the inverse of the matrix $ A = \begin{pmatrix} 1 & 2 & -3 \\ 3 & -2 & 2 \\ 4 & 1 & 2 \end{pmatrix} $ by using elementary row operations. Thus, $ A $ is invertible. Use the inverse to solve the system\[\begin{align*}x + 2y - 3z &= a \\3x - 2y + 2z &= b \\4x + y + 2z &= c\end{align*}\]for all $ a, b, c $. Express the solution as a linear combination of the column vectors of $ A^{-1} $. Notice since the matrix of coefficients $ A $ is invertible, the system has a unique solution.

Consider the matrix A=12−33−22412 We have to find the inverse of matrix A by elementary row…

(1 -3 Find the inverse of the matrix A = 3 -2 by using elementary row oper- 4 1 2 ations. Thus, A is invertible. Use the inverse to solve the system х + 2у — 32 — а 3x – 2y + 2z = b 4x + y + 2z = c for all a, b, c. Express the solution as a linear combination of the column vectors of A-1. Notice since the matrix of coefficients A is invertible, the system has a unique solution.

(1 -3 Find the inverse of the matrix A = 3 -2 by using elementary row oper- 4 1 2 ations. Thus, A is invertible. Use the inverse to solve the system х + 2у — 32 — а 3x – 2y + 2z = b 4x + y + 2z = c for all a, b, c. Express the solution as a linear combination of the column vectors of A-1. Notice since the matrix of coefficients A is invertible, the system has a unique solution.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(3) Find the inverse of the matrix $ A = \begin{pmatrix} 1 & 2 & -3 \\ 3 & -2 & 2 \\ 4 & 1 & 2 \end{pmatrix} $ by using elementary row operations. Thus, $ A $ is invertible. Use the inverse to solve the system

\[
\begin{align*}
x + 2y - 3z &= a \\
3x - 2y + 2z &= b \\
4x + y + 2z &= c
\end{align*}
\]

for all $ a, b, c $. Express the solution as a linear combination of the column vectors of $ A^{-1} $. Notice since the matrix of coefficients $ A $ is invertible, the system has a unique solution.

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