O-LevelAdditional MathematicsSimultaneous equations4037/12 · Oct/Nov 2013 · Q119 Marks
It is given that the matrix A = [[2, 3], [4, 1]].
- (a)It is given that the matrix A = [[2, 3], [4, 1]].
- (a)(i)Find A + 2I.[1]
- (a)(ii)Find A².[2]
- (a)(iii)Using your answer to part (ii) find the matrix B such that A²B = I.[2]
- (b)Given that the matrix C = [[x, -1], [x²-x+1, x-1]], show that det C ≠ 0.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.
- [B1] (a) (i) [[4, 3], [4, 3]]
- [B1, B1] (a) (ii) for any 2 correct elements [[16, 9], [12, 13]]
- [B1] for all correct
- [√B1, √B1] (a) (iii) Follow through on their A²
- [M1] (b) for attempt to obtain det C
- [A1] for this correct quadratic expression from a correct det C (2x² - 2x + 1)
- [DM1] for use of discriminant or attempt to solve using the formula, or attempt to complete the square in order to show there are no real roots.
- [A1] for correct reasoning or statement that there are no real roots.
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