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The matrix$$ \mathbf{A} = \begin{pmatrix} 3 & -2 \\ 1 & 0 \end{pmatrix} $$has eigenvalues \(\lambda_1 = 2\) and \(\lambda_2 = 1\) with corresponding eigenvectors$$\mathbf{x}_1 = \begin{pmatrix} 2 \\ 1 \end{pmatrix}\quad\text{and}\quad\mathbf{x}_2 = \begin{pmatrix} 1 \\ 1 \end{pmatrix}.$$Show that \(\mathbf{P} = (\mathbf{x}_1 \mid \mathbf{x}_2)\) diagonalises \(\mathbf{A}\).
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