Vectors and Matrices II

No calculator

Original questions written at exam standard. Work each one before you open the solution.

Difficulty

Question 1 Foundation

Find the determinant of

\begin{pmatrix} 5 & 2 \\ 4 & 3 \end{pmatrix}

Question 2 Foundation

Explain why

\begin{pmatrix} 3 & 6 \\ 1 & 2 \end{pmatrix}

has no inverse.

Question 3 Standard

\overrightarrow{OA} = \mathbf{a}

and

\overrightarrow{OB} = \mathbf{b}

. Write

\overrightarrow{AB}

in terms of

\mathbf{a}

and

\mathbf{b}

Question 4 Standard

Find the inverse of

\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}

Question 5 Stretch

M

is the midpoint of

AB

, where

\overrightarrow{OA} = \mathbf{a}

and

\overrightarrow{OB} = \mathbf{b}

. Find

\overrightarrow{OM}

Question 6 Stretch

Find the image of

(4, -1)

under the transformation with matrix

\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}

, and name the transformation.