Use Gauss-Jordan method to find A^-1, if it exists. Check your answer by finding AA^-1 and A^-1A.

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asked May 14, 2023 44.9k views

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Kthevar · Answer 1 · 2023-05-21T10:12:26+0000

ANSWER:

There is no inverse matrix

Explanation:

We have the following matrix:

$A=\begin{bmatrix}{-5} & {-5} & {0} \\ {0} & {-5} & {-5} \\ {4} & {0} & {-4}\end{bmatrix}$

The first thing we must do is calculate the determinant of the matrix in order to know whether or not it has an inverse:

$\begin{gathered} \det A=\mleft\lbrace-5\cdot\mleft(-5\mright)\cdot\mleft(-4\mright)\mright\rbrace+\mleft\lbrace-5\cdot\mleft(-5\mright)\cdot4\mright\rbrace+\mleft\lbrace0\cdot0\cdot0\mright\rbrace-\mleft\lbrace0\cdot\mleft(-5\mright)\cdot4\mright\rbrace-\mleft\lbrace-5\cdot\mleft(-5\mright)\cdot0\mright\rbrace-\mleft\lbrace-5\cdot0\cdot\mleft(-4\mright)\mright\rbrace \\ \det A=-100+100+0-0-0-0 \\ \det A=0 \end{gathered}$

Since the determinant of A is 0, it means that it has no inverse

Use Gauss-Jordan method to find A^-1, if it exists. Check your answer by finding AA^-1 and A^-1A.

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