User:

Multiply a matrix by a scalar

You can multiply any matrix by a constant called a scalar. When you do this, you multiply each individual element by the value of the scalar. This operation is called scalar multiplication.

To multiply a matrix by a scalar k, multiply each element by k.

k·A = kA

$\fs2k\left[\begin{array}a&b\\c&d\end{array}\right]\;=\;\left[\begin{array}ka&kb\\kc&kd\end{array}\right]$

$\fs23\left[\begin{array}4&1\\7&-2\end{array}\right]\;=\;\left[\begin{array}3(4)&3(1)\\3(7)&3(-2)\end{array}\right]\;=\;\left[\begin{array}12&3\\21&-6\end{array}\right]$

Calculate:

 $8\left[\begin{matrix}4&-3\\-1&5\end{matrix}\right]=$