Sec 4 E-Math · Matrices

Order and elements questions with answers

Practice questions on order and elements, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

State the order of the matrix $\begin{pmatrix} 4 \\ -1 \\ -2 \\ -3 \end{pmatrix}$ .

Step 1 of 3

Count the rows (each row runs across)

\text{Rows} = 4

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Questions

Question 1The order of a matrix
State the order of the matrix $\begin{pmatrix} 3 & -3 \end{pmatrix}$ .
Show the worked solution
1. Step 1: Count the rows (each row runs across) $\text{Rows} = 1$
2. Step 2: Count the columns (each column runs down) $\text{Columns} = 2$
3. Step 3: Write the order of the matrixOrder $= 1 \mathbin{\times} 2$
Question 2The order of a matrix
State the order of the matrix $\begin{pmatrix} 0 \\ 3 \end{pmatrix}$ .
Show the worked solution
1. Step 1: Count the rows (each row runs across) $\text{Rows} = 2$
2. Step 2: Count the columns (each column runs down) $\text{Columns} = 1$
3. Step 3: Write the order of the matrixOrder $= 2 \mathbin{\times} 1$
Question 3Reading an element
$A = \begin{pmatrix} 4 & 9 & -5 \\ 10 & 10 & 6 \\ 3 & 10 & -2 \end{pmatrix}$ . Write down the element in the third row and second column of $A$ .
Show the worked solution
1. Step 1: Go to row 3 $\text{Row } 3: \; 3, \; 10, \; -2$
2. Step 2: Take its element in column 2 $\text{Element} = 10$
Question 4Reading an element
$A = \begin{pmatrix} 6 & 11 \\ 8 & -3 \end{pmatrix}$ . Write down the element in the first row and first column of $A$ .
Show the worked solution
1. Step 1: Go to row 1 $\text{Row } 1: \; 6, \; 11$
2. Step 2: Take its element in column 1 $\text{Element} = 6$
Question 5Information as a matrix
Class 4A has 8 boys, 7 girls and 8 teachers. Class 4B has 5 boys, 4 girls and 7 teachers. Write down a matrix showing this information, with one row for each class and one column for each group, in the order given.
Show the worked solution
1. Step 1: Row 1: Class 4A $8 \quad 7 \quad 8$
2. Step 2: Row 2: Class 4B $5 \quad 4 \quad 7$
3. Step 3: Put the rows together as one matrix $\begin{pmatrix} 8 & 7 & 8 \\ 5 & 4 & 7 \end{pmatrix}$
Question 6Information as a matrix
Ali bought 9 pens, 9 files and 8 rulers. Ben bought 7 pens, 9 files and 12 rulers. Write down a matrix showing this information, with one row for each person and one column for each item, in the order given.
Show the worked solution
1. Step 1: Row 1: Ali $9 \quad 9 \quad 8$
2. Step 2: Row 2: Ben $7 \quad 9 \quad 12$
3. Step 3: Put the rows together as one matrix $\begin{pmatrix} 9 & 9 & 8 \\ 7 & 9 & 12 \end{pmatrix}$

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Questions

Question 1The order of a matrix

State the order of the matrix $\begin{pmatrix} 3 & -3 \end{pmatrix}$ .

Show the worked solution

Step 1: Count the rows (each row runs across) $\text{Rows} = 1$
Step 2: Count the columns (each column runs down) $\text{Columns} = 2$
Step 3: Write the order of the matrixOrder $= 1 \mathbin{\times} 2$

Question 2The order of a matrix

State the order of the matrix $\begin{pmatrix} 0 \\ 3 \end{pmatrix}$ .

Show the worked solution

Step 1: Count the rows (each row runs across) $\text{Rows} = 2$
Step 2: Count the columns (each column runs down) $\text{Columns} = 1$
Step 3: Write the order of the matrixOrder $= 2 \mathbin{\times} 1$

Question 3Reading an element

$A = \begin{pmatrix} 4 & 9 & -5 \\ 10 & 10 & 6 \\ 3 & 10 & -2 \end{pmatrix}$ . Write down the element in the third row and second column of $A$ .

Show the worked solution

Step 1: Go to row 3 $\text{Row } 3: \; 3, \; 10, \; -2$
Step 2: Take its element in column 2 $\text{Element} = 10$

Question 4Reading an element

$A = \begin{pmatrix} 6 & 11 \\ 8 & -3 \end{pmatrix}$ . Write down the element in the first row and first column of $A$ .

Show the worked solution

Step 1: Go to row 1 $\text{Row } 1: \; 6, \; 11$
Step 2: Take its element in column 1 $\text{Element} = 6$

Question 5Information as a matrix

Class 4A has 8 boys, 7 girls and 8 teachers. Class 4B has 5 boys, 4 girls and 7 teachers. Write down a matrix showing this information, with one row for each class and one column for each group, in the order given.

Show the worked solution

Step 1: Row 1: Class 4A $8 \quad 7 \quad 8$
Step 2: Row 2: Class 4B $5 \quad 4 \quad 7$
Step 3: Put the rows together as one matrix $\begin{pmatrix} 8 & 7 & 8 \\ 5 & 4 & 7 \end{pmatrix}$

Question 6Information as a matrix

Ali bought 9 pens, 9 files and 8 rulers. Ben bought 7 pens, 9 files and 12 rulers. Write down a matrix showing this information, with one row for each person and one column for each item, in the order given.

Show the worked solution

Step 1: Row 1: Ali $9 \quad 9 \quad 8$
Step 2: Row 2: Ben $7 \quad 9 \quad 12$
Step 3: Put the rows together as one matrix $\begin{pmatrix} 9 & 9 & 8 \\ 7 & 9 & 12 \end{pmatrix}$