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Matrices - Addition and Subtraction of Matrices

Matrices - Addition and Subtraction of Matrices

Secondary 4

It is given that \(\mathbf{P} = \begin{pmatrix} -5 & -3 \\ 1 & 5 \end{pmatrix}\) and \(\mathbf{Q} = \begin{pmatrix} 2a & 1 \\ 1 & -3b \end{pmatrix}\).

  1. Evaluate \(\mathbf{P}^2\).
  2. If \(\mathbf{Q} - \mathbf{P}^2 = \begin{pmatrix} -10 & 1 \\ 1 & 8 \end{pmatrix}\), find the values of \(a\) and \(b\).

Solution:

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Answer:(a) \(P^2=\begin{pmatrix}22&0\\0&22\end{pmatrix}\); (b) \(a=6,b=-10\).

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