Find the inverse of the following matrices by the adjoining method

Engineering

Mathematics

Inverse of a Matrix

Introduction to Determinants

Properties of Determinant

Question

Find the inverse of the following matrices by the adjoining method
$[\begin{array}{cc} - 1 & 5 \\ - 3 & 2 \end{array}]$

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M [\begin{array}{cc} - 1 & 5 \\ - 3 & 2 \end{array}]

M = [\begin{array}{ll} a b \\ c d \end{array}], M^{- 1} = \frac{1}{| M |} [\begin{array}{cc} d & - b \\ - c & a \end{array}]

adj (M)

adj(M) =

[\begin{array}{cc} 2 & - 5 \\ 3 & - 1 \end{array}]

and |M| = – 2 + 15

= 13

∴ M^{- 1} = \frac{1}{13} [\begin{array}{cc} 2 & - 5 \\ 3 & - 1 \end{array}]