Matrices Worksheets 1.1: Matrix Arithmetic

A worksheet and solution on adding and subtracting matrices.

Introduction

During the COVID-19 pandemic I created some worksheets based on A Level Maths and Further Maths. I’ve decided to upload these to my blog in case they can be of use.

Matrix Arithmetic

1. Write down the size of the following matrices.

   1. \[ \begin{pmatrix} 1 & 0 & 1 \\ x & y & z \end{pmatrix} \]

   2. \[ \begin{pmatrix} -4 & 2 \\ 0 & 1 \end{pmatrix} \]

   3. \[ \begin{pmatrix} 1 & 4 & -1 & 0\\ -4 & 1 & -3 & 8 \\ 2 & 0 & -8 & 3 \end{pmatrix} \]

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2. Given the following matrices:

\[ \text{A} = \begin{pmatrix} 1 & 2 & -1 \\ 0 & 4 & 1 \\ 4 & 6 & -4 \end{pmatrix}, \]
\[ \text{B} = \begin{pmatrix} 0 & 4& 1\\ 2 & -6 & 0 \\ \end{pmatrix}, \]
\[ \text{C} = \begin{pmatrix} -6 & 7 & -3\\ 2& 0 & -1\\ 3 & 4 & -9\\ \end{pmatrix}. \]

Calculate, where defined.

1. A + C

2. C - 2B

3. A + B

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3. Calculate the following matrix sums.

1. \[ \begin{pmatrix} 1 & 2\\ 3& 4\\ \end{pmatrix} + 2\begin{pmatrix} 4 & 8\\ 0& -1\\ \end{pmatrix} \]
2. \[ \begin{pmatrix} 0 & -8 & 6 \\ 0 & -3 & 4 \\ -6 & 0 & 2 \\ \end{pmatrix} - \begin{pmatrix} 1 & 2 & 7 \\ 6 & -5 & 4 \\ 1 & 4 & -1 \\ \end{pmatrix} \]
3. \[ \begin{pmatrix} a & -1 & 2 \\ 9 & -1 & 3 \\ -4 & -2 & 0 \\ 3 & -3 & b \\ \end{pmatrix} -2 \begin{pmatrix} -4 & 6 & 0 \\ 3 & c & -1 \\ 0 & -3 & d \\ 4 & 2 &-6 \\ \end{pmatrix} \]

Solutions

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