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1 markMatrix Problem Solving

CSEC Mathematics · May/June 2007 · Paper 2 · Question 14(a)(iv)

A, B and C are three 2x2 matrices such that A = ((a, b), (c, d)), B = ((5, 3), (3, 2)) and C = ((14, 0), (-9, 5)).

Find the value of a, b, c and d given that 3A + B⁻¹ = C.

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Other parts of this question

  1. 14(a)(i)Find 3A.[7 marks]
  2. 14(a)(ii)Find B⁻¹.[1 mark]
  3. 14(a)(iii)Find 3A + B⁻¹.[1 mark]
  4. 14(b)(i)a)Describe in words, the geometric transformation J which maps EFGH onto E'F'G'H'.[8 marks]
  5. 14(b)(i)b)Describe in words, the geometric transformation K which maps E'F'G'H' onto E''F''G''H''.[1 mark]
  6. 14(b)(ii)a)Write the matrix which represents the transformation described above as J.[1 mark]
  7. 14(b)(ii)b)Write the matrix which represents the transformation described above as K.[1 mark]
  8. 14(b)(iii)The point P (6, 2) is mapped onto P' by the transformation J. State the co-ordinates of P'.[1 mark]
  9. 14(b)(iv)The point Q (5, -4) is mapped onto Q' by the transformation K. State the co-ordinates of Q'.[1 mark]

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