Scalar Multiplication

Find $3\times \left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$.

• 1Multiply every element by $3$: $1\times 3=3$, $2\times 3=6$, $3\times 3=9$, $4\times 3=12$

Answer: $\left[\begin{array}{cc}3& 6\\ 9& 12\end{array}\right]$

Find $-2\times \left[\begin{array}{cc}2& -1\\ 0& 5\end{array}\right]$.

• 1Multiply every element by $-2$: $2\times (-2)=-4$, $-1\times (-2)=2$, $0\times (-2)=0$, $5\times (-2)=-10$

Answer: $\left[\begin{array}{cc}-4& 2\\ 0& -10\end{array}\right]$

Find $4\times \left[\begin{array}{cc}1& 0\\ 2& 3\\ -1& 5\end{array}\right]$.

• 1Multiply every entry by $4$.
• 2Result is still order $3\times 2$.

Answer: $\left[\begin{array}{cc}4& 0\\ 8& 12\\ -4& 20\end{array}\right]$