Consider the matrices A = \begin{bmatrix} 1 & 6 \\ -2 & 2 \\ 8 & 0 \end{bmatrix} \text{and } B = \begin{bmatrix} 3 & -1 & 5 \\ 2 & 4 & 7 \end{bmatrix}.

State the dimensions of matrix A.

State the dimensions of matrix B.

Is A + B possible?

Consider the matrices A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \text{, }B = \begin{bmatrix} a \\ b \end{bmatrix} \text{and } C = \begin{bmatrix} a & b \end{bmatrix}.

State the dimensions of matrix A.

State the dimensions of matrix B.

State the dimensions of matrix C.

Is A + B possible?

Is B - C possible?

Consider the matrices:

A = \begin{bmatrix} 1 & 5 & 3 \\ 2 & -1 & 6 \\ 10 & 7 & 8 \end{bmatrix} \text {, } B = \begin{bmatrix} 2 & -4 & 1 \\ 8 & 3 & -9 \\ 11 & 12 & 0 \end{bmatrix} \text{and } C = \begin{bmatrix} 1 & -6 \\ 5 & 9 \end{bmatrix}

State the dimensions of matrix A.

State the dimensions of matrix B.

State the dimensions of matrix C.

Is A + B possible?

Is A + B - C possible?

Consider the matrices: A = B = C = \begin{bmatrix} a & b \\ c & d \\ e & f \\ g & h \end{bmatrix}

State the dimensions of matrix A.

State the dimensions of matrix B.

State the dimensions of matrix C.

Is C - B possible?

Is C + A - B possible?

Find A + B, if:

A = \begin{bmatrix} 2 & 5 \\ 4 & 3 \end{bmatrix} and B = \begin{bmatrix} 5 & 4 \\ -1 & 6 \end{bmatrix}

A = \begin{bmatrix} -1 \\ 5 \\ 7 \end{bmatrix} and B = \begin{bmatrix} 2 \\ 4 \\ -3 \end{bmatrix}

A = \begin{bmatrix} 1 & \frac{5}{2} & 8 \\ 5 & -7 & 10 \end{bmatrix} and B = \begin{bmatrix} 2 & \frac{3}{2} & 9 \\ -3 & 0 & 7 \end{bmatrix}

A = \begin{bmatrix} 4 & 8 \\ 5 & 10 \\ -2 & 6 \end{bmatrix} and B = \begin{bmatrix} 1 & 9 \\ -4 & 2 \\ 3 & -1 \end{bmatrix}

A = \begin{bmatrix} 5 & 2 & 8 \\ 6 & 10 & -3 \\ 1 & -2 & 6 \end{bmatrix} and B = \begin{bmatrix} 1 & 5 & 9 \\ 4 & 6 & -2 \\ 1 & 3 & -1 \end{bmatrix}

Find A - B, if:

A = \begin{bmatrix} 1 & 4 \\ 5 & 2 \end{bmatrix} and B = \begin{bmatrix} 8 & 0 \\ -1 & 7 \end{bmatrix}

A = \begin{bmatrix} -2 \\ 4 \\ 3 \end{bmatrix} and B = \begin{bmatrix} 8 \\ 0 \\ -3 \end{bmatrix}

A = \begin{bmatrix} -\frac{1}{3} & 7 & 12 \\ 11 & -3 & 0 \end{bmatrix} and B = \begin{bmatrix} \frac{2}{3} & 1 & 0 \\ 4 & 8 & 7 \end{bmatrix}

A = \begin{bmatrix} 6 & 7 \\ 9 & 10 \\ 4 & -6 \end{bmatrix} and B = \begin{bmatrix} 2 & 5 \\ -1 & 3 \\ 6 & 1 \end{bmatrix}

A = \begin{bmatrix} 7 & 4 & 2 \\ 11 & 10 & 8 \\ 9 & 3 & 7 \end{bmatrix} and B = \begin{bmatrix} 5 & -3 & 1 \\ 5 & 3 & 2 \\ 0 & 4 & -1 \end{bmatrix}

A = \begin{bmatrix} 3.6 & 7.4 \\ 8.9 & 10.5 \\ 4.7 & -6.3 \end{bmatrix} and B = \begin{bmatrix} 1.8 & 5.1 \\ 0.9 & 5.2 \\ -6.1 & 1.5 \end{bmatrix}

A = \begin{bmatrix} 75 & 42 & 21 & 54 \\ 18 & 27 & 81 & 56 \\ 93 & 36 & 72 & 49 \end{bmatrix} and B = \begin{bmatrix} 51 & -32 & 18 & 21 \\ 56 & 39 & 24 & 57\\ 18 & 27 & -19 & 32 \end{bmatrix}

Matrix equations

Solve the following matrix equations for x:

\begin{bmatrix} 5 & x \\ -2 & 9 \end{bmatrix} + \begin{bmatrix} 7 & 3 \\ 8 & 2 \end{bmatrix} = \begin{bmatrix} 12 & 8 \\ 6 & 11 \end{bmatrix}

\begin{bmatrix} 10 & 8 \\ -4 & 10 \end{bmatrix} - \begin{bmatrix} 8 & 3 \\ 2x & 7 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ -14 & 3 \end{bmatrix}

\begin{bmatrix} 11 & 7 \\ -x & 10 \\ 4 & 9 \end{bmatrix} - \begin{bmatrix} 6 & 2 \\ -8 & -1 \\ 0 & -3 \end{bmatrix} = \begin{bmatrix} 5 & 5 \\ 9 & 11 \\ 4 & 12 \end{bmatrix}

Consider the following matrix equation:

\begin{bmatrix} u - 3 & 2v & 9 \\ 3x & 7 & 10 \end{bmatrix} + \begin{bmatrix} 4u & v & -3w \\ 10 & 5 & 27 \end{bmatrix} = \begin{bmatrix} 47 & 12 & 18 \\ 31 & 6y & 37 \end{bmatrix}

Find the value of:

Applications

The following table shows the number of visitors to a website by country:

	Australia	New Zealand	Thailand	China
January	37	25	29	41
February	26	35	19	51
March	32	22	18	27
April	30	28	24	37
May	31	20	24	28

Find the total number of visitors to the site during each month. Express your answer as a column matrix, where the rows describe the months in order of the given table.

Find how many more visitors were from China than from Thailand each month by subtracting an appropriate pair of column matrices. Express your answer as a column matrix, where the rows describe the months in order of the given table.

The tables below show the number of fruit and vegetables sold at Mohamad's three corner shops over a particular weekend.

Saturday:

	Fruit	Vegetables
Shop 1	58	29
Shop 2	48	71
Shop 3	54	38

Sunday:

	Fruit	Vegetables
Shop 1	45	32
Shop 2	40	62
Shop 3	38	46

Write the sales of fruit and vegetables for Saturday as a 3 \times 2 matrix.

Write the sales of fruit and vegetables for Sunday as a 3 \times 2 matrix.

Add your matrices to find the total number of sales of fruit and vegetables for each shop over the entire weekend. Express your answers as a 3 \times 2 matrix.

Outcomes

U1.AoS3.3

matrix arithmetic: the definition of addition, subtraction, multiplication by a scalar, multiplication, the power of a square matrix, and the conditions for their use

U1.AoS3.9

add and subtract matrices, multiply a matrix by a scalar or another matrix, and raise a matrix to a power

6.03 Addition and subtraction of matrices

Outcomes

U1.AoS3.3

U1.AoS3.9

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