﻿ Multiplying Matrices Worksheets | Problems & Solutions

# Multiplying Matrices Worksheets

Multiplying Matrices Worksheets
• Page 1
1.
A = $\left(\begin{array}{cc}5& - 1\\ 0& 4\end{array}\right)$ and I = $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$. What is AI?
 a. $\left(\begin{array}{cc}5& 0\\ 0& 4\end{array}\right)$ b. $\left(\begin{array}{cc}4& 0\\ - 1& 5\end{array}\right)$ c. $\left(\begin{array}{cc}5& - 1\\ 0& 4\end{array}\right)$ d. $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$

2.
P = $\left(\begin{array}{ccc}4& 5& 5\\ 3& - 4& 0\end{array}\right)$ and Q = $\left(\begin{array}{cc}- 1& 9\\ 5& - 9\\ 4& 0\end{array}\right)$. Find PQ.
 a. $\left(\begin{array}{cc}41& 4\\ 0& 45\end{array}\right)$ b. $\left(\begin{array}{cc}0& 4\\ 0& 63\end{array}\right)$ c. Not defined d. $\left(\begin{array}{cc}41& -9\\ - 23& 63\end{array}\right)$

3.
If A = $\left(\begin{array}{cc}2& 4\end{array}\right)$ and B = $\left(\begin{array}{c}7\\ 3\end{array}\right)$, then find AB.
 a. $\left(\begin{array}{c}26\end{array}\right)$ b. $\left(\begin{array}{c}14\\ 12\end{array}\right)$ c. $\left(\begin{array}{cc}2& 7\\ 4& 3\end{array}\right)$ d. $\left(\begin{array}{cc}15& 15\end{array}\right)$

4.
If A = $\left(\begin{array}{cc}20& - 12\\ 8& 0\end{array}\right)$, then the matrix $\frac{1}{4}$A is?
 a. $\left(\begin{array}{cc}5& 3\\ 2& 0\end{array}\right)$ b. $\left(\begin{array}{cc}5& - 3\\ 2& 0\end{array}\right)$ c. $\left(\begin{array}{cc}20& - 3\\ 8& 0\end{array}\right)$ d. $\left(\begin{array}{cc}5& - 12\\ 2& 0\end{array}\right)$

5.
Find the scalar product of - 3 and the square matrix $\left(\begin{array}{cc}2& 0\\ - 4& 2\end{array}\right)$.
 a. $\left(\begin{array}{cc}- 6& 0\\ 12& - 6\end{array}\right)$ b. $\left(\begin{array}{cc}- 3& 0\\ 3& 3\end{array}\right)$ c. $\left(\begin{array}{cc}- 2& - 2\\ - 4& 0\end{array}\right)$ d. $\left(\begin{array}{cc}- 2& 2\\ - 2& 0\end{array}\right)$

6.
If X = $\left(\begin{array}{cc}6& - 2\\ 3& 0\end{array}\right)$ and Y = $\left(\begin{array}{cc}4& - 3\\ - 2& 2\end{array}\right)$, then find 3Y - 5X.
 a. $\left(\begin{array}{cc}- 18& 5\\ 21& 2\end{array}\right)$ b. $\left(\begin{array}{cc}5& 6\\ 1& - 2\end{array}\right)$ c. $\left(\begin{array}{cc}- 18& 1\\ - 21& 6\end{array}\right)$ d. $\left(\begin{array}{cc}18& -7\\ 1& - 6\end{array}\right)$

7.
If X = $\left(\begin{array}{cc}8& - 3\\ 4& 0\end{array}\right)$ and Y = $\left(\begin{array}{cc}5& - 4\\ - 3& 3\end{array}\right)$, then find 4Y - 8X.
 a. $\left(\begin{array}{cc}44& -9\\ 8& - 12\end{array}\right)$ b. $\left(\begin{array}{cc}8& 8\\ 8& - 3\end{array}\right)$ c. $\left(\begin{array}{cc}- 44& 8\\ - 44& 12\end{array}\right)$ d. $\left(\begin{array}{cc}- 44& 8\\ 44& 3\end{array}\right)$

8.
If C = $\left(\begin{array}{ccc}4& 9& 4\\ 8& 0& 4\end{array}\right)$ and B = $\left(\begin{array}{ccc}4& 6& 10\\ 0& 4& 8\end{array}\right)$, then which of the following represents the matrix 4C + 5B?
 a. $\left(\begin{array}{ccc}16& 36& 50\\ 32& 20& 56\end{array}\right)$ b. $\left(\begin{array}{ccc}36& 66& 16\\ 0& 0& 56\end{array}\right)$ c. $\left(\begin{array}{ccc}20& 66& 16\\ 32& 20& 56\end{array}\right)$ d. $\left(\begin{array}{ccc}36& 66& 66\\ 32& 20& 56\end{array}\right)$

9.
If C = $\left(\begin{array}{ccc}4& 8& 3\\ 7& 0& 3\end{array}\right)$ and B = $\left(\begin{array}{ccc}3& 9& 9\\ 0& 3& 7\end{array}\right)$ , then which of the following is the matrix 3C + 4B?
 a. $\left(\begin{array}{ccc}12& 24& 36\\ 21& 12& 37\end{array}\right)$ b. $\left(\begin{array}{ccc}12& 60& 9\\ 21& 12& 37\end{array}\right)$ c. $\left(\begin{array}{ccc}24& 60& 45\\ 21& 12& 37\end{array}\right)$ d. $\left(\begin{array}{ccc}24& 60& 9\\ 0& 0& 37\end{array}\right)$

If A = $\left(\begin{array}{cc}2& - 1\\ 0& 1\end{array}\right)$ and B = $\left(\begin{array}{cc}5& 2\\ 6& - 4\end{array}\right)$, then find the matrix A + 2B.
 a. $\left(\begin{array}{cc}12& - 4\\ 12& 7\end{array}\right)$ b. $\left(\begin{array}{cc}- 12& 1\\ 6& - 2\end{array}\right)$ c. $\left(\begin{array}{cc}8& 4\\ 8& 0\end{array}\right)$ d. $\left(\begin{array}{cc}12& 3\\ 12& - 7\end{array}\right)$