Hint
Check matrix dimensions before multiplying. Subtract the off-diagonal product from the main-diagonal product.
Worked solution
(a)
\(7(8)-2=54\)
Answer: \(54\).
Answer: \(54\)
(b)
\(Av=\left[\begin{matrix}50\\76\end{matrix}\right]\)
Answer: \(50\).
Answer: \(50\)
(c)
\(\displaystyle A^{-1}=\left[\begin{matrix}\frac{4}{27} & - \frac{1}{54}\\- \frac{1}{27} & \frac{7}{54}\end{matrix}\right]\)
Answer: \(\displaystyle - \frac{1}{54}\).
Answer: \(\displaystyle - \frac{1}{54}\)
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: Subtract the off-diagonal product from the main-diagonal product.
- 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 multiply entries position by position to form a matrix product.
(b) · 2 marks
- 1 mark: Take the first row of A times v.
- 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: Area scale is |det A|, while signed orientation depends on det A.
(c) · 2 marks
- 1 mark: Swap the diagonal entries and negate the off-diagonal entries before dividing by det A.
- 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 multiply entries position by position to form a matrix product.
Total: 6 marks.