1. The problem is to multiply the matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) by the scalar 3.
2. The formula for scalar multiplication of a matrix is to multiply each element of the matrix by the scalar:
$$ 3 \times \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} 3a & 3b \\ 3c & 3d \end{bmatrix} $$
3. This means each element in the matrix is multiplied by 3 individually.
4. So the resulting matrix after multiplication is:
$$ \begin{bmatrix} 3a & 3b \\ 3c & 3d \end{bmatrix} $$
This is the final answer.
Matrix Scalar Multiplication 534A36
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.