Using elementary transformations, find the inverse of each of the matrices,

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Using elementary transformations, find the inverse of each of the matrices,
$[\begin{array}{ll} 4 5 \\ 3 4 \end{array}]$

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A = IA

$[\begin{array}{cc} 2 & 5 \\ 1 & 3 \end{array}] = [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] A$
R₂ $\leftrightarrow$ R₂ – 2R₁
$[\begin{array}{cc} 1 & 3 \\ 2 & 5 \end{array}] = [\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}] A$

R₂ → R₂ – 2R₁
$[\begin{array}{cc} 1 & 3 \\ 0 & - 1 \end{array}] = [\begin{array}{cc} 0 & 1 \\ 1 & - 2 \end{array}] A$
R₂ → – (R₂)
$[\begin{array}{cc} 1 & 3 \\ 0 & 1 \end{array}] = [\begin{array}{cc} 0 & 1 \\ 1 & 2 \end{array}] A \Rightarrow R_{1} \to R_{1} - 3 R_{2}$
= $[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] = [\begin{array}{cc} 3 & - 5 \\ - 1 & 2 \end{array}] A$
$∴ A^{- 1} = [\begin{array}{cc} 3 & - 5 \\ - 1 & 2 \end{array}]$

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