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

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Inverse of a Matrix

Question

Find the inverse of the following matrix by using elementary row transformation :
$[\begin{array}{cc} 3 & 10 \\ 2 & 7 \end{array}]$

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Let

A = [\begin{array}{cc} 3 & 10 \\ 2 & 7 \end{array}]

We can write A = IA

[\begin{array}{cc} 3 & 10 \\ 2 & 7 \end{array}] = [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] A

R₁ → R₁ – R₂

[\begin{array}{cc} 1 & 3 \\ 2 & 7 \end{array}] = [\begin{array}{cc} 1 & - 1 \\ 0 & 1 \end{array}] A

R₂ → R₂ – 2R₁

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

R₁ → R₁ – 3R₂

[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] = [\begin{array}{cc} 7 & - 10 \\ - 2 & 3 \end{array}] A

∴ A^{- 1} = [\begin{array}{cc} 7 & - 10 \\ - 2 & 3 \end{array}]