Adjugate matrix calculation

Questions specifically asking to find the adjugate (adjoint) matrix of a 3×3 matrix.

1 questions · Standard +0.3

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WJEC Further Unit 4 2022 June Q10
9 marks Standard +0.3
The matrix \(\mathbf{A}\) is defined by $$\mathbf{A} = \begin{pmatrix} 4 & 8 & 0 \\ 0 & \lambda & -2 \\ 4 & 0 & \lambda \end{pmatrix}.$$
  1. Show that there are two values of \(\lambda\) for which \(\mathbf{A}\) is singular. [4]
  2. Given that \(\lambda = 3\),
    1. determine the adjugate matrix of \(\mathbf{A}\),
    2. determine the inverse matrix \(\mathbf{A}^{-1}\). [5]