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then A-1 Given b 18 = = = [4] solve Az = b 8 4= [B]₁ A

then A-1 Given b 18 = = = [4] solve Az = b 8 4= [B]₁ A

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Given the matrix \( A \) and the vector \( \vec{b} \): \[ A = \begin{bmatrix} -1 & 8 \\ -5 & -9 \end{bmatrix}, \] we need to find the inverse of matrix \( A \) and solve the system of linear equations \( A\vec{x} = \vec{b} \) where \[ \vec{b} = \begin{bmatrix} -1 \\ 2 \end{bmatrix}. \] First, find the inverse \( A^{-1} \): \[ A^{-1} = \begin{bmatrix} \, \, \, & \, \, \, \\ \, \, \, & \, \, \, \end{bmatrix}. \] Then, given the vector \( \vec{b} \), solve the system \( A\vec{x} = \vec{b} \) to find the vector \( \vec{x} \): \[ \vec{x} = \begin{bmatrix} \, \, \, \\ \, \, \, \end{bmatrix}. \]
Transcribed Image Text:Given the matrix \( A \) and the vector \( \vec{b} \): \[ A = \begin{bmatrix} -1 & 8 \\ -5 & -9 \end{bmatrix}, \] we need to find the inverse of matrix \( A \) and solve the system of linear equations \( A\vec{x} = \vec{b} \) where \[ \vec{b} = \begin{bmatrix} -1 \\ 2 \end{bmatrix}. \] First, find the inverse \( A^{-1} \): \[ A^{-1} = \begin{bmatrix} \, \, \, & \, \, \, \\ \, \, \, & \, \, \, \end{bmatrix}. \] Then, given the vector \( \vec{b} \), solve the system \( A\vec{x} = \vec{b} \) to find the vector \( \vec{x} \): \[ \vec{x} = \begin{bmatrix} \, \, \, \\ \, \, \, \end{bmatrix}. \]
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