Matrix Basics Worksheet

This worksheet covers the Matrix Basics lessons: What Is a Matrix?, Matrix Addition and Subtraction, Scalar Multiplication, Matrix Multiplication, The Identity Matrix, The Determinant of a $2\times 2$ Matrix, Singular Matrices, and The Determinant of a $3\times 3$ Matrix.

There are $10$ questions in each of the $8$ sections ($80$ questions in total). Show your working where a calculation is involved. Work on paper, then check against the lessons if you get stuck.

Q1. State the order of the matrix below.

$\left[\begin{array}{ccc}4& -1& 7\\ 2& 5& 0\end{array}\right]$

Q2. State the order of the matrix below.

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

Q3. State the order of the matrix below.

$\left[\begin{array}{cccc}5& 2& 0& -3\end{array}\right]$

Q4. State the order of the matrix below.

$\left[\begin{array}{c}2\\ 7\\ -3\\ 0\\ 5\end{array}\right]$

Q5. A matrix has order $6\times 2$. How many elements does it have?

Q6. A matrix has order $4\times 4$. How many elements does it have?

Q7. For the matrix below, write down the element in row $2$, column $3$.

$\left[\begin{array}{cccc}9& 4& -2& 0\\ 1& -5& 6& 3\end{array}\right]$

Q8. For the matrix below, write down the element in row $3$, column $1$.

$\left[\begin{array}{ccc}2& 5& -1\\ 0& 4& 7\\ -6& 3& 9\end{array}\right]$

Q9. A matrix has $20$ elements arranged in $4$ rows. How many columns does it have?

Q10. A matrix has $24$ elements arranged in $6$ columns. How many rows does it have?

Q1. Find $A+B$.

$A=\left[\begin{array}{cc}3& 5\\ 2& -1\end{array}\right]$, $B=\left[\begin{array}{cc}1& 4\\ 6& 0\end{array}\right]$

Q2. Find $A-B$.

$A=\left[\begin{array}{cc}7& -2\\ 0& 3\end{array}\right]$, $B=\left[\begin{array}{cc}2& 5\\ -4& 1\end{array}\right]$

Q3. Find $A+B$.

$A=\left[\begin{array}{ccc}2& 0& 4\\ -1& 3& 5\end{array}\right]$, $B=\left[\begin{array}{ccc}1& 6& -2\\ 4& 0& 3\end{array}\right]$

Q4. Find $A-B$.

$A=\left[\begin{array}{cc}9& 1\\ 3& -4\end{array}\right]$, $B=\left[\begin{array}{cc}2& 6\\ -1& 5\end{array}\right]$

Q5. Find $A+B$.

$A=\left[\begin{array}{ccc}0& 3& -1\\ 5& 2& 4\end{array}\right]$, $B=\left[\begin{array}{ccc}6& -2& 3\\ 1& 0& -5\end{array}\right]$

Q6. Find $B-A$.

$A=\left[\begin{array}{cc}-3& 4\\ 8& -6\end{array}\right]$, $B=\left[\begin{array}{cc}5& -1\\ 2& 3\end{array}\right]$

Q7. Find $A+B$.

$A=\left[\begin{array}{cc}10& -5\\ 3& 7\end{array}\right]$, $B=\left[\begin{array}{cc}4& 2\\ -6& 1\end{array}\right]$

Q8. Find $A-B$.

$A=\left[\begin{array}{ccc}4& -3& 2\\ 1& 5& -6\end{array}\right]$, $B=\left[\begin{array}{ccc}-2& 0& 7\\ 3& -4& 1\end{array}\right]$

Q9. Find $A+B$.

$A=\left[\begin{array}{cc}8& -1\\ 0& 6\end{array}\right]$, $B=\left[\begin{array}{cc}-3& 5\\ 2& -2\end{array}\right]$

Q10. Find $A+A$.

$A=\left[\begin{array}{cc}2& -3\\ 4& 1\end{array}\right]$

Q1. Find $3A$.

$A=\left[\begin{array}{cc}2& 5\\ -3& 4\end{array}\right]$

Q2. Find $-2A$.

$A=\left[\begin{array}{cc}6& -2\\ 0& 7\end{array}\right]$

Q3. Find $4A$.

$A=\left[\begin{array}{ccc}1& 4& -3\\ 5& 0& 2\end{array}\right]$

Q4. Find $\frac{1}{5}A$.

$A=\left[\begin{array}{cc}10& -15\\ 20& 5\end{array}\right]$

Q5. Find $0\times A$.

$A=\left[\begin{array}{cc}3& -1\\ 2& 6\end{array}\right]$

Q6. Find $-1\times A$.

$A=\left[\begin{array}{cc}-4& 2\\ 8& -6\end{array}\right]$

Q7. Find $5A$.

$A=\left[\begin{array}{cc}2& -1\\ 0& 3\end{array}\right]$

Q8. Find $6A$.

$A=\left[\begin{array}{cc}5& -3\\ 2& 4\end{array}\right]$

Q9. Find $6A$.

$A=\left[\begin{array}{cc}7& 2\\ -3& 5\end{array}\right]$

Q10. Find $-3A$.

$A=\left[\begin{array}{cc}-2& 7\\ 6& -1\end{array}\right]$

Q1. Find $AB$.

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$, $B=\left[\begin{array}{cc}2& 0\\ 1& 3\end{array}\right]$

Q2. Find $AB$.

$A=\left[\begin{array}{cc}2& -1\\ 0& 3\end{array}\right]$, $B=\left[\begin{array}{cc}4& 1\\ 2& 5\end{array}\right]$

Q3. Find $AB$.

$A=\left[\begin{array}{cc}0& 2\\ -1& 3\end{array}\right]$, $B=\left[\begin{array}{cc}4& 1\\ 2& -2\end{array}\right]$

Q4. Find $AB$.

$A=\left[\begin{array}{cc}3& 1\\ -2& 4\end{array}\right]$, $B=\left[\begin{array}{cc}1& 2\\ 0& -1\end{array}\right]$

Q5. Find $AB$.

$A=\left[\begin{array}{ccc}1& 2& 0\\ 3& -1& 4\end{array}\right]$, $B=\left[\begin{array}{cc}2& 1\\ 0& 3\\ -1& 2\end{array}\right]$

Q6. Find $BA$.

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$, $B=\left[\begin{array}{cc}2& 0\\ 1& 3\end{array}\right]$

Q7. Find $AB$.

$A=\left[\begin{array}{cc}5& 2\\ -1& 3\end{array}\right]$, $B=\left[\begin{array}{cc}0& 4\\ 6& -2\end{array}\right]$

Q8. Find $AB$.

$A=\left[\begin{array}{ccc}1& 2& -1\\ 0& 3& 2\end{array}\right]$, $B=\left[\begin{array}{cc}2& 0\\ 1& -1\\ 3& 4\end{array}\right]$

Q9. Find $A^2$ (that is, $A\times A$).

$A=\left[\begin{array}{cc}2& 0\\ 1& -3\end{array}\right]$

Q10. Find $A^2$ (that is, $A\times A$).

$A=\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right]$

Q1. Write down the $2\times 2$ identity matrix.

Q2. Write down the $3\times 3$ identity matrix.

Q3. Find $AI$, where $I$ is the $2\times 2$ identity matrix.

$A=\left[\begin{array}{cc}4& -2\\ 3& 5\end{array}\right]$

Q4. Find $IB$, where $I$ is the $2\times 2$ identity matrix.

$B=\left[\begin{array}{cc}7& 1\\ 0& -2\end{array}\right]$

Q5. Write down the $4\times 4$ identity matrix.

Q6. Find $IC$, where $I$ is the $3\times 3$ identity matrix.

$C=\left[\begin{array}{ccc}2& 0& -1\\ 3& 1& 4\\ 0& -2& 5\end{array}\right]$

Q7. Find $DI$, where $I$ is the $3\times 3$ identity matrix.

$D=\left[\begin{array}{ccc}1& -3& 2\\ 0& 4& -1\\ 5& 0& 2\end{array}\right]$

Q8. Find $EI$, where $I$ is the $3\times 3$ identity matrix.

$E=\left[\begin{array}{ccc}6& 1& -2\\ 0& 3& 4\\ -1& 0& 5\end{array}\right]$

Q9. Find $IF$, where $I$ is the $2\times 2$ identity matrix.

$F=\left[\begin{array}{cc}9& -4\\ 2& 6\end{array}\right]$

Q10. Find $GI$, where $I$ is the $2\times 2$ identity matrix.

$G=\left[\begin{array}{cc}3& 8\\ -5& 1\end{array}\right]$

Q1. Find the determinant of the matrix below.

$\left[\begin{array}{cc}3& 4\\ 2& 5\end{array}\right]$

Q2. Find the determinant of the matrix below.

$\left[\begin{array}{cc}6& -2\\ 1& 3\end{array}\right]$

Q3. Find the determinant of the matrix below.

$\left[\begin{array}{cc}0& 5\\ 4& -1\end{array}\right]$

Q4. Find the determinant of the matrix below.

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

Q5. Find the determinant of the matrix below.

$\left[\begin{array}{cc}7& 7\\ 2& 2\end{array}\right]$

Q6. Find the determinant of the matrix below.

$\left[\begin{array}{cc}10& 3\\ 4& 1\end{array}\right]$

Q7. Find the determinant of the matrix below.

$\left[\begin{array}{cc}5& 0\\ 0& 5\end{array}\right]$

Q8. Find the determinant of the matrix below.

$\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right]$

Q9. Find the determinant of the matrix below.

$\left[\begin{array}{cc}8& 3\\ 5& 2\end{array}\right]$

Q10. Find the determinant of the matrix below.

$\left[\begin{array}{cc}-2& 6\\ 3& -4\end{array}\right]$

Q1. Is the matrix below singular? Show your working.

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

Q2. Is the matrix below singular? Show your working.

$\left[\begin{array}{cc}3& 1\\ 2& 5\end{array}\right]$

Q3. Is the matrix below singular? Show your working.

$\left[\begin{array}{cc}6& 3\\ 4& 2\end{array}\right]$

Q4. Is the matrix below singular? Show your working.

$\left[\begin{array}{cc}9& 4\\ 2& 1\end{array}\right]$

Q5. Is the matrix below singular? Show your working.

$\left[\begin{array}{cc}0& 0\\ 5& 7\end{array}\right]$

Q6. Find the value of $k$ that makes the matrix below singular.

$\left[\begin{array}{cc}k& 4\\ 3& 6\end{array}\right]$

Q7. Find the value of $m$ that makes the matrix below singular.

$\left[\begin{array}{cc}2& m\\ 4& 6\end{array}\right]$

Q8. Is the matrix below singular? Show your working.

$\left[\begin{array}{cc}4& 6\\ 2& 3\end{array}\right]$

Q9. Is the matrix below singular? Show your working.

$\left[\begin{array}{cc}7& 2\\ 3& 1\end{array}\right]$

Q10. Find the value of $n$ that makes the matrix below singular.

$\left[\begin{array}{cc}5& n\\ 2& 4\end{array}\right]$

Q1. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 4\\ 5& 6& 0\end{array}\right]$

Q2. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}2& 0& 1\\ 3& 1& 0\\ 1& 2& 4\end{array}\right]$

Q3. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right]$

Q4. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}3& 1& 2\\ 0& 2& 1\\ 1& 0& 3\end{array}\right]$

Q5. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}2& -1& 0\\ 1& 3& 2\\ 0& 1& 1\end{array}\right]$

Q6. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}1& 1& 1\\ 2& 2& 2\\ 3& 1& 4\end{array}\right]$

Q7. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}4& 0& 0\\ 0& 5& 0\\ 0& 0& 2\end{array}\right]$

Q8. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}1& 2& 0\\ 3& 0& 1\\ 0& 1& 2\end{array}\right]$

Q9. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}2& 3& 1\\ 0& 1& 4\\ 1& 0& 2\end{array}\right]$

Q10. Find the determinant of the matrix below.

$\left[\begin{array}{ccc}2& 1& 3\\ 1& 0& 2\\ 4& 1& 5\end{array}\right]$