A-LevelFurther MathematicsProof by induction9231/12 · May/June 2023 · Q17 Marks
Let A = ((3, 0), (1, 1))
- (a)Prove by mathematical induction that, for all positive integers n, 2A^n = ((2x3^n, 0), (3^n-1, 2))[5]
- (b)Find, in terms of n, the inverse of A^n.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- B1 States base case.
- B1 States inductive hypothesis.
- M1A1 Multiplies 2A^k with A.
- A1 States conclusion.
- B1 det A^n = 3^n
- B1 OE A^-n = 2*3^-n * ((2, 0), (1-3^n, 2*3^n)) seen.
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