Find inverse, by elementary row operations (if possible), of the following matrix:

$[\begin{matrix} 1 & - 3 - 2 & 6 \end{matrix}]$

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Solution

Let $A = [\begin{matrix} 1 & - 3 - 2 & 6 \end{matrix}]$

In order to use elementary row operations, we write A = IA

$\Rightarrow [\begin{matrix} 1 & - 3 - 2 & 6 \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] A$

$\Rightarrow [\begin{matrix} 1 & - 3 0 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 2 & 1 \end{matrix}] A$ $[∵ R_{2} \to R_{2} + 2 R_{1}]$

Since, we obtain all zeroes in a row of the matrix A on LHS, $A^{- 1}$ does not exist.

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Find inverse, by elementary row operations (if possible), of the following matrix: [1−3−26]

Let A=[1−3−26] In order to use elementary row operations, we write A = IA ⇒[1−3−26]=[1001]A ⇒[1−300]=[1021]A [∵R2→R2+2R1] Since, we obtain all zeroes in a row of the matrix A on LHS, A−1 does not exist.

Find inverse, by elementary row operations (if possible), of the following matrix:

$[\begin{matrix} 1 & - 3 - 2 & 6 \end{matrix}]$