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Matrices - Addition and Subtraction of Matrices

Matrices - Addition and Subtraction of Matrices

Secondary 4

It is given that \(\mathbf{P} = \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix}\) and \(\mathbf{Q} = \begin{pmatrix} 3 & 3 \\ -2 & 4 \end{pmatrix}\) and \(\mathbf{R} = \begin{pmatrix} 20 \\ 10 \end{pmatrix}\).

  1. Compute
    1. \(\mathbf{P}^2\),
    2. \(\mathbf{PQ}\),
    3. \(\mathbf{QR}\).
  2. Find the value of \(k\) if \(\mathbf{P}^2 + k\mathbf{P} = \mathbf{PQ}\).

Solution:

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Answer:(a)(i) \(\begin{pmatrix}-5&9\\-6&-2\end{pmatrix}\); (ii) \(\begin{pmatrix}-3&15\\-10&2\end{pmatrix}\); (iii) \(\begin{pmatrix}90\\0\end{pmatrix}\); (b) \(k=2\).

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