Find the adjoint of the matrix A = .

Engineering

Mathematics

Transpose and Adjoint of a Matrix

Inverse of a Matrix

Introduction to Determinants

Question

Find the adjoint of the matrix A = $[\begin{array}{ccc} 1 & 4 & 3 \\ 4 & 2 & 1 \\ 3 & 2 & 2 \end{array}]$ .

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

Here,

C₁₁ = (4 – 2) = 2

C₁₂ = – (8 – 3) = – 5

C₁₃ = (8 – 6) = 2

C₂₁ = – (8 – 6) = – 2

C₂₂ = (2 – 9) = – 7

C₃₁ = (4 – 6) = – 2

C₃₂ = – (1 – 12) = 11

C₃₃ = (2 – 16) = – 14

Hence,

adjA = [\begin{array}{ccc} C_{11} & C_{21} & C_{31} \\ C_{12} & C_{22} & C_{32} \\ C_{13} & C_{23} & C_{33} \end{array}] = [\begin{array}{ccc} 2 & - 2 & - 2 \\ - 5 & - 7 & 11 \\ 2 & 10 & - 14 \end{array}]