Find the inverse of the following matrices by the adjoining method

Engineering

Mathematics

Introduction to Matrix

Transpose and Adjoint of a Matrix

Inverse of a Matrix

Question

Find the inverse of the following matrices by the adjoining method
$[\begin{array}{ccc} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & - 1 \end{array}]$

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M = [\begin{array}{ccc} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & - 1 \end{array}]

(M) = 1(3(–1) – 0)

= (– 3)

$adj (m) = = [\begin{array}{ccc} - 3 & 0 & 0 \\ - 3 & - 1 & 0 \\ - 9 & - 2 & 3 \end{array}]$

$m^{- 1} = \frac{1}{- 3} [\begin{array}{ccc} - 3 & 0 & 0 \\ - 3 & - 1 & 0 \\ - 9 & - 2 & 3 \end{array}]$

$M^{- 1} = [\begin{array}{ccc} 1 & 0 & 0 \\ 1 & 1 / 3 & 0 \\ 3 & 2 / 3 & - 1 \end{array}]$