If , then adj (P)

Engineering

Mathematics

Transpose and Adjoint of a Matrix

Question

If $P = [\begin{array}{cc} 1 & 4 \\ 2 & 6 \end{array}]$ , then adj (P)

$[\begin{array}{cc} 1 & 4 \\ 2 & 6 \end{array}]$

$[\begin{array}{cc} 6 & - 4 \\ - 2 & 1 \end{array}]$

$[\begin{array}{cc} 6 & - 2 \\ - 4 & 1 \end{array}]$

$[\begin{array}{cc} 2 & 1 \\ 6 & 4 \end{array}]$

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Cofactor of the martix is

[\begin{array}{cc} M_{11} & - M_{12} \\ - M_{21} & M_{22} \end{array}]

Where M₁₁ = 6

M₁₂ = 2

M₂₁ = 4

M₂₂ = 1

Substituting all value we get

Cofactor of the matrix as

[\begin{array}{cc} 6 & - 2 \\ - 4 & 1 \end{array}]

The adjoint of the matrix is transpose of cofactor of the given matrix

∴ Adjoint of the matrix is

[\begin{array}{cc} 6 & - 4 \\ - 2 & 1 \end{array}]

Hence the answer is option B.