Matrices: Practice Questions

Given the matrix \( \mathbf{M} = \begin{pmatrix} 4 & -2 \\ 0 & 3 \end{pmatrix} \), find the resulting matrix of the operation:
\( 3\mathbf{M} - \begin{pmatrix} 2 & 1 \\ -5 & 4 \end{pmatrix} \)

Given the matrices \( P = \begin{pmatrix} 2 & 3 \end{pmatrix} \) and \( Q = \begin{pmatrix} 1 \\ -4 \end{pmatrix} \), find the product matrix \( PQ \).

Given that \( \begin{pmatrix} 2 & x \\ 1 & 4 \end{pmatrix} \begin{pmatrix} 3 \\ -2 \end{pmatrix} = \begin{pmatrix} 10 \\ y \end{pmatrix} \), find the value of \( x + y \).

Given the matrices \( \mathbf{A} = \begin{pmatrix} 3 & -1 \\ 2 & 4 \end{pmatrix} \) and \( \mathbf{B} = \begin{pmatrix} 2 \\ 5 \end{pmatrix} \), calculate the matrix product \( \mathbf{AB} \).

Given the matrices \( \mathbf{A} = \begin{pmatrix} 1 & 2 \\ 0 & -3 \end{pmatrix} \) and \( \mathbf{B} = \begin{pmatrix} 4 \\ -1 \end{pmatrix} \), calculate the product matrix \( \mathbf{AB} \).

Given matrices \( \mathbf{A} = \begin{pmatrix} 2 & -1 \\ 0 & 3 \end{pmatrix} \) and \( \mathbf{B} = \begin{pmatrix} 1 & 4 \\ -2 & 5 \end{pmatrix} \), find the matrix \( 2\mathbf{A} + \mathbf{B} \).