If , find A–1 by elementary transformation.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Inverse of a Matrix

Question

If $A = [\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}]$ , find A^–1 by elementary transformation.

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Given,

A = [\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}]

Noe, A + IA

[\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}] = [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] A

R₂ → R₂ – 3R₁

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

R₁ → R₁ + R₂

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

R₂ → R₂/2

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

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