[Legacy] Matrices

Given that $\mathbf{A}$ does not have an inverse, find the exact values of $x$.

Write down the order of matrix $\mathbf{B}$.

The matrix $\mathbf{BC} = \begin{pmatrix} 9 & -12 & 15 \\ 3 & -8 & -3 \\ 6 & -3 & 20 \end{pmatrix}$. Explain why $\mathbf{CB} \neq \mathbf{BC}$.

State the order of the matrix $\begin{pmatrix} 0 & 1 & 4 & 8 \\ 5 & 8 & 1 & 6 \end{pmatrix}$.

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

Hence, given that $\mathbf{ABA} = \mathbf{I}$, find the matrix $\mathbf{B}$.

$\mathbf{A} = \begin{pmatrix} 2 & -1 \\ 1 & -3 \end{pmatrix} \quad\text{and}\quad \mathbf{B} = \begin{pmatrix} 0 & -2 \\ 3 & -5 \end{pmatrix}.$

Find $(\mathbf{BA})^{-1}$.

State the order of the matrix $\mathbf{C}$.

Find the matrix $\mathbf{X}$.

$\mathbf{A}^{-1}$,

the matrix $\mathbf{C}$ such that $\mathbf{CA} = \mathbf{B}$,

the matrix $\mathbf{D}$ such that $\mathbf{A}^{-1}\mathbf{D} + \mathbf{B} = \mathbf{I}$.

Given that $\mathbf{L} = \begin{pmatrix} 1 & 1 & 1 & 1 \end{pmatrix}$, construct a matrix, $\mathbf{M}$, of the number of tickets sold, such that the matrix product $\mathbf{LM}$ can be found.

Find the matrix product $\mathbf{LM}$.

State what information is represented by the matrix product $\mathbf{LM}$.

An adult ticket costs $5, a student ticket costs $4 and a child ticket costs $3.

Construct a matrix, $\mathbf{N}$, of the ticket costs, such that the matrix product $\mathbf{LMN}$ can be found and state what information is represented by the matrix product $\mathbf{LMN}$.

Find $(2\mathbf{A})^{-1}$.

Hence solve the simultaneous equations

Find the matrix $\mathbf{C}$ such that $\mathbf{C} = 3\mathbf{A} + \mathbf{B}$.

Show that $\det(\mathbf{AB}) = \det \mathbf{A} \times \det \mathbf{B}$.

Find the matrix $(\mathbf{AB})^{-1}$.

Find a relationship connecting the constants $p$ and $q$.

Given that $p$ and $q$ are positive and that $\det\mathbf{A} = -3p$, find the value of $p$ and of $q$.

Find the matrix $\mathbf{A}$ if

State, without evaluation, what is represented by the matrix $\mathbf{QP}$.

Given that the matrix $\mathbf{R} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$, state, without evaluation, what is represented by the matrix $\mathbf{QPR}$.

Write down a matrix, $\mathbf{P}$, for the numbers of passengers and a matrix, $\mathbf{Q}$, of single ticket prices, such that the matrix product $\mathbf{QP}$ can be found.

Find the matrix product $\mathbf{QP}$.

Given that $\mathbf{R} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$, explain what information is found by evaluating the matrix product $\mathbf{QPR}$.