Find the inverse of the following matrix by using elementary row transformation:

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Find the inverse of the following matrix by using elementary row transformation:
$[\begin{array}{cc} 5 & 2 \\ 2 & 1 \end{array}]$

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Given :

A = [\begin{array}{cc} 5 & 2 \\ 2 & 1 \end{array}]

In order to use row elementary transformation we write A = AI.

[\begin{array}{cc} 5 & 2 \\ 2 & 1 \end{array}] = A [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}]

R₁ → R₁ – 2R₂

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

R₂ → R₂ – 2R₁

[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] = A [\begin{array}{cc} 1 & - 2 \\ - 2 & 5 \end{array}]

∴ A^{- 1} = [\begin{array}{cc} 1 & - 2 \\ - 2 & 5 \end{array}]

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