[Legacy] Matrices

Complete matrix $\mathbf{M}$ to represent this information.

Using an algebraic method, find the value of $x$ and the value of $y$.
Show your working.

$x$ = ______
$y$ = ______

Explain what each element in $\mathbf{P}$ represents.

______

$\mathbf{BA}$,

______

$\mathbf{B}^{-1}$.

______

Given that $\mathbf{A} + 2\mathbf{C} = 3\mathbf{B}$, find $\mathbf{C}$.

______

Calculate $2\mathbf{B} - 3\mathbf{A}$.

Calculate $\mathbf{BC}$.

Calculate $\mathbf{A}^{-1} + \mathbf{A}$.

Evaluate $2\mathbf{A} - \mathbf{B}$.

Find $\mathbf{A}^2$.

Find $\mathbf{B}^{-1}$.

$\mathbf{A} + \mathbf{Z} = \mathbf{A}$

Find $\mathbf{Z}$.

$\mathbf{M} + 2\mathbf{I} = \mathbf{B}$, where $\mathbf{I}$ is the $2 \times 2$ identity matrix.

Find $\mathbf{M}$.

Find $\mathbf{A} + 2\mathbf{B}$.

Find $\mathbf{AB}$.

Find $x$ and $y$.

$x$ = ______ , $y$ = ______

Find $\mathbf{B}^{-1}$.

$2\mathbf{A} - \mathbf{B}$,

______

$\mathbf{B}^{-1}$.

______

The matrix $\mathbf{C}$ satisfies the following equation.

Find $\mathbf{C}$.

______

Find $\mathbf{D}$.

______

Explain the meaning of the information given by matrix $\mathbf{D}$.

______

Find the total amount, in dollars, that Theresa gets for the fruit she sells.

$ ______

Express as a single matrix

______

Express as a single matrix

______

Find $\mathbf{A}^{-1}$.

______

$\mathbf{B} + 3\mathbf{I} = \mathbf{A}$ where $\mathbf{I}$ is the $2 \times 2$ identity matrix.

Find $\mathbf{B}$.

______

Find $x$ and $y$.

$x$ = ______
$y$ = ______

the image of (1, 0) under the transformation A,

( ______ , ______ )

the image of (0, 1) under the transformation A.

( ______ , ______ )

The transformation B maps (1, 0) onto (1, 3) and (0, 1) onto (-3, -2).

Write down the matrix that represents transformation B.

Describe fully the transformation given by the matrix $\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$.

______

Find the matrix that represents this transformation.

Answer ______

On the grid above, draw and label triangle $C$.

Find the matrix that represents the inverse transformation that maps triangle $C$ onto triangle $B$.

Answer ______

Find the ratio area of triangle $C$ : area of triangle $B$.

______ : ______

Find the matrix that represents the single transformation that maps triangle $A$ onto triangle $C$.

Answer ______

Anya sells all of these T-shirts to a shop.
She charges $5 for each small T-shirt, $6 for each medium T-shirt and $8 for each large T-shirt.

Represent these amounts in a $3 \times 1$ column matrix $\mathbf{N}$.

$\mathbf{N}$ = ______

Work out $\mathbf{P} = \mathbf{MN}$.

$\mathbf{P}$ = ______

Explain what the elements in matrix $\mathbf{P}$ represent.

______

Work out

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