Hint
Check matrix dimensions before multiplying. Subtract the off-diagonal product from the main-diagonal product.
Worked solution
(a)
\(10(11)-2=108\)
Answer: \(108\).
Answer: \(108\)
(b)
\(Av=\left[\begin{matrix}101\\139\end{matrix}\right]\)
Answer: \(101\).
Answer: \(101\)
(c)
\(\displaystyle A^{-1}=\left[\begin{matrix}\frac{11}{108} & - \frac{1}{108}\\- \frac{1}{54} & \frac{5}{54}\end{matrix}\right]\)
Answer: \(\displaystyle - \frac{1}{108}\).
Answer: \(\displaystyle - \frac{1}{108}\)
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.