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[ 2 Find the inverse of the invertible matrix A = 5 -2

[ 2 Find the inverse of the invertible matrix A = 5 -2

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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**Matrix Inversion Problem** Determine the inverse of the invertible matrix \( A \) given by: \[ A = \begin{bmatrix} 2 & -1 \\ 5 & -2 \end{bmatrix} \] The inverse of \( A \) is represented by \( A^{-1} \), and we need to find: \[ A^{-1} = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix} \] To find the inverse of a \( 2 \times 2 \) matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), the formula is: \[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \] Make sure the determinant \( ad - bc \neq 0 \) to ensure the matrix is invertible.
Transcribed Image Text:**Matrix Inversion Problem** Determine the inverse of the invertible matrix \( A \) given by: \[ A = \begin{bmatrix} 2 & -1 \\ 5 & -2 \end{bmatrix} \] The inverse of \( A \) is represented by \( A^{-1} \), and we need to find: \[ A^{-1} = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix} \] To find the inverse of a \( 2 \times 2 \) matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), the formula is: \[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \] Make sure the determinant \( ad - bc \neq 0 \) to ensure the matrix is invertible.
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