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

Engineering

Mathematics

Algebra of Matrices

Inverse of a Matrix

Question

Using elementary transformations, find the inverse of each of the matrices,
$[\begin{array}{cc} 6 & - 3 \\ - 2 & 1 \end{array}]$

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[\begin{array}{cc} 6 & - 3 \\ - 2 & 1 \end{array}] = [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] A

R₁ → 1/6R₁

[\begin{array}{cc} 1 & - 1 / 2 \\ - 2 & 1 \end{array}] = [\begin{array}{cc} 1 / 6 & 0 \\ 0 & 1 \end{array}] A

R₂ → R₂ + 2R₁

[\begin{array}{cc} 1 & - 1 / 2 \\ 0 & 0 \end{array}] = [\begin{array}{cc} 1 / 6 & 0 \\ 1 / 3 & 1 \end{array}] A

As the matrix on LHS contain 0 only in the second row the given matrix is non-invertible i.e. A^–1 does not exist.