Hint
State the column-vector convention and order of composition. Take the absolute determinant of the transformation.
Worked solution
(a)
\(|\det A|=108\)
Answer: \(108\).
Answer: \(108\)
(b)
\(\displaystyle 9m+ 10m^{2}= 12m\implies m= \frac{12- 9}{10}= \frac{3}{10}\)
Answer: \(\displaystyle \frac{3}{10}\).
Answer: \(\displaystyle \frac{3}{10}\)
(c)
\(AB=\left[\begin{matrix}19 & 10\\12 & 12\end{matrix}\right]\)
Answer: \(19\).
Answer: \(19\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Take the absolute determinant of the transformation.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not confuse an invariant line with a line of fixed points.
(b) · 2 marks
- 1 mark: Equate the output slope to the original slope, keeping the separate horizontal direction.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Check the vertical direction separately from slope m.
(c) · 2 marks
- 1 mark: Multiply A by B in the stated order.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not confuse an invariant line with a line of fixed points.
Total: 6 marks.