If A = \(\begin{pmatrix}a & b \\c & d \\\end{pmatrix}\)th

1.	If A = \(\begin{pmatrix}a & b \\c & d \\\end{pmatrix}\)then adj A = ?((a,b),(c,d))A. \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\)B. \(\begin{pmatrix}-d & b \\c & -a \\\end{pmatrix}\)C. \(\begin{pmatrix}d &-b \\-c & a \\\end{pmatrix}\)D.\(\begin{pmatrix}-d &-b \\c & a \\\end{pmatrix}\)
Answer» To find adj A we will first find the cofactor matrix C₁₁ = d C₁₂ = -c C₂₁= -b C₂₂ = a Cofactor matrix A = \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\) Adj A = \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\) = \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\)

If A = \(\begin{pmatrix}a & b \\c & d \\\end{pmatrix}\)then adj A = ?((a,b),(c,d))A. \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\)B. \(\begin{pmatrix}-d & b \\c & -a \\\end{pmatrix}\)C. \(\begin{pmatrix}d &-b \\-c & a \\\end{pmatrix}\)D.\(\begin{pmatrix}-d &-b \\c & a \\\end{pmatrix}\)

Answer»

To find adj A we will first find the cofactor matrix

C₁₁ = d C₁₂ = -c

C₂₁= -b C₂₂ = a

Cofactor matrix A = \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\)

Adj A = \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\)

= \(\begin{pmatrix}d& -c \\-b & a \\\end{pmatrix}\)