matrices practice

Answer 1

1. Add the following matrices:

Matrix A:
\[ \begin{bmatrix} 3 & 5 \\ 2 & 7 \end{bmatrix} \]

Matrix B:
\[ \begin{bmatrix} 1 & 2 \\ 4 & 6 \end{bmatrix} \]

Solution:

\[ \begin{bmatrix} 3 & 5 \\ 2 & 7 \end{bmatrix} + \begin{bmatrix} 1 & 2 \\ 4 & 6 \end{bmatrix} = \begin{bmatrix} 4 & 7 \\ 6 & 13 \end{bmatrix} \]

2. Subtract the following matrices:

Matrix X:
\[ \begin{bmatrix} 9 & 4 \\ 5 & 1 \end{bmatrix} \]

Matrix Y:
\[ \begin{bmatrix} 2 & 1 \\ 3 & 6 \end{bmatrix} \]

Solution:

\[ \begin{bmatrix} 9 & 4 \\ 5 & 1 \end{bmatrix} - \begin{bmatrix} 2 & 1 \\ 3 & 6 \end{bmatrix} = \begin{bmatrix} 7 & 3 \\ 2 & -5 \end{bmatrix} \]

3. Multiply the following matrices:

Matrix P:
\[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]

Matrix Q:
\[ \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \]

Solution:

\[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \times \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} = \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix} \]