If A = \( \begin{pmatrix}2&-1 \\1 &3\end{pmatrix}\), then A-1 = ?A.

1.	If A = \( \begin{pmatrix}2&-1 \\1 &3\end{pmatrix}\), then A-1 = ?A.\( \begin{pmatrix}3/7&-1/7 \\1/7 &2/7\end{pmatrix}\)B.\( \begin{pmatrix}3/7&1/7 \\-1/7 &2/7\end{pmatrix}\)C.\( \begin{pmatrix}1/3&1/7 \\1/7 &2/7\end{pmatrix}\)D. None of these
Answer» 1 = 1/\|A\| adj A --------- 1 \|A\| = 3 x 2 – (1) x (-1) = 7 C₁₁ = 3 C₁₂ = -1 C₂₁ = 1 C₂₂ = 2 Cofactor matrix A = \( \begin{pmatrix} 2&1 \\ 4 &3 \end{pmatrix}\) Adj A = \( \begin{pmatrix} 3&-1 \\ 1 &2 \end{pmatrix}\) = \( \begin{pmatrix} 3&1 \\ -1 &2 \end{pmatrix}\) Putting in 1 A^-1 = 1/\|7\| \( \begin{pmatrix} 3&1 \\ -1 &2 \end{pmatrix}\) = \( \begin{pmatrix} 3/7&1/7 \\ -1/7 &2/7 \end{pmatrix}\)

If A = \( \begin{pmatrix}2&-1 \\1 &3\end{pmatrix}\), then A-1 = ?A.\( \begin{pmatrix}3/7&-1/7 \\1/7 &2/7\end{pmatrix}\)B.\( \begin{pmatrix}3/7&1/7 \\-1/7 &2/7\end{pmatrix}\)C.\( \begin{pmatrix}1/3&1/7 \\1/7 &2/7\end{pmatrix}\)D. None of these

Answer»

1 = 1/|A| adj A --------- 1

|A| = 3 x 2 – (1) x (-1)

= 7

C₁₁ = 3 C₁₂ = -1

C₂₁ = 1 C₂₂ = 2

Cofactor matrix A = \( \begin{pmatrix} 2&1 \\ 4 &3 \end{pmatrix}\)

Adj A = \( \begin{pmatrix} 3&-1 \\ 1 &2 \end{pmatrix}\)

= \( \begin{pmatrix} 3&1 \\ -1 &2 \end{pmatrix}\)

Putting in 1

A^-1 = 1/|7| \( \begin{pmatrix} 3&1 \\ -1 &2 \end{pmatrix}\)

= \( \begin{pmatrix} 3/7&1/7 \\ -1/7 &2/7 \end{pmatrix}\)