[Legacy] Matrices

Write down two matrices whose product under matrix multiplication will give the total number of points awarded to each team.

Evaluate the matrix product from part (i) and hence state which team was awarded the most points.

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

Hence find the matrix $\mathbf{C}$ such that $\mathbf{A}\mathbf{C} = \mathbf{B}$.

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

Hence find, in radians, the acute angles $x$ and $y$ such that

Find the inverse of the matrix $\begin{pmatrix} 4 & -2 \\ -5 & 3 \end{pmatrix}$.

Hence solve the simultaneous equations

Find the values of the constant $a$ for which $\mathbf{A}^{-1}$ does not exist.

Given that $a = 4$, find $\mathbf{A}^{-1}$.

Hence find the matrix $\mathbf{B}$ such that $\mathbf{AB} = \begin{pmatrix}2 & 3 \\ 4 & -5\end{pmatrix}$.

state the order of $\mathbf{A}$,

find $\mathbf{C}$.

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

Using $\mathbf{X}^{-1}$, find the coordinates of the point of intersection of the lines

Given that $\mathbf{A} = \begin{pmatrix} 4 & -1 \\ a & b \end{pmatrix}$, $\mathbf{B} = \begin{pmatrix} 2 & 3 \\ -5 & 4 \end{pmatrix}$ and $\mathbf{AB} = \begin{pmatrix} 13 & 8 \\ 18 & 4 \end{pmatrix}$, find the value of $a$ and of $b$.

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

Hence find $\mathbf{Z}$.

Given the matrices $\mathbf{A} = \begin{pmatrix} -1 & 2 \\ 3 & 0 \end{pmatrix}$ and $\mathbf{B} = \begin{pmatrix} 3 & 0 \\ 1 & 2 \end{pmatrix}$, find $\mathbf{A}^2 - 2\mathbf{B}$.

Using a matrix method, solve the equations

Matrices $\mathbf{X}$, $\mathbf{Y}$ and $\mathbf{Z}$ are such that

Write down all the matrix products which are possible using any two of these matrices. Do not evaluate these products.

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

Hence find $\mathbf{C}$.

Given that the matrix $\mathbf{X} = \begin{pmatrix} 2 & -4 \\ k & 0 \end{pmatrix}$, find $\mathbf{X}^2$ in terms of the constant $k$.

Given that the matrix $\mathbf{A} = \begin{pmatrix} a & 1 \\ b & 5 \end{pmatrix}$ and the matrix $\mathbf{A}^{-1} = \begin{pmatrix} \frac{5}{6} & -\frac{1}{6} \\ -\frac{2}{3} & \frac{1}{3} \end{pmatrix}$, find the value of each of the integers $a$ and $b$.