Find the matrix A such that

Engineering

Mathematics

Introduction to Matrix

Inverse of a Matrix

Question

Find the matrix A such that $[\begin{array}{cc} 5 & - 7 \\ - 2 & 3 \end{array}] . A = [\begin{array}{cc} - 16 & - 6 \\ 7 & 2 \end{array}]$

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Given $[\begin{array}{cc} 5 & - 7 \\ - 2 & 3 \end{array}] . A = [\begin{array}{cc} - 16 & - 6 \\ 7 & 2 \end{array}]$

Applying Row transformations

R₂ → 2R₁ + 5R₂

[\begin{array}{cc} 5 & - 7 \\ 0 & 1 \end{array}] . A = [\begin{array}{cc} - 16 & - 6 \\ 3 & - 2 \end{array}]

R₁ → R₁ + 7R₂

[\begin{array}{cc} 5 & 0 \\ 0 & 1 \end{array}] . A = [\begin{array}{cc} 5 & - 20 \\ 3 & - 2 \end{array}]

R_{1} \to \frac{R_{1}}{5}

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

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

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

(∵ A.I = I.A = A)