Answered: -2 1] 10 A = -5

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.4: Subtracting Real Numbers

Problem 62WE

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Question

Find the inverse of the shown matrix A, if possible. Check that AA^-1 = I₂ and A^-1A = I₂.

Expert Solution

Step 1

Consider the following matrix:

$A = [\begin{matrix} 10 & - 2 \\ - 5 & 1 \end{matrix}]$

Find the determinant of matrix A:

$\begin{array}{rcl} |A| & = & |\begin{matrix} 10 & - 2 \\ - 5 & 1 \end{matrix}| \\ = & (10 \times 1) - [(- 2) \times (- 5)] \\ = & 10 - 10 \\ = & 0 \end{array}$

$|A| = 0$

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