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1 markMatrix Problem Solving

CSEC Mathematics · May/June 2005 · Paper 2 · Question 14(a)(iv)

Given matrix M = [[2, 5], [7, 15]].

Pre-multiply both sides of the following matrix equation by M⁻¹: [[2, 5], [7, 15]] * [[x], [y]] = [[-3], [17]]. Hence solve for x and y.

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Other parts of this question

  1. 14(a)(i)Show that M is a non-singular matrix.[7 marks]
  2. 14(a)(ii)Write down the inverse of M.[1 mark]
  3. 14(a)(iii)Write down the 2x2 matrix which is equal to the product M x M⁻¹.[1 mark]
  4. 14(b)(i)Write down the 2x2 matrix, R, which represents a reflection in the y-axis.[8 marks]
  5. 14(b)(ii)Write down the 2x2 matrix, N, which represents a clockwise rotation of 180° about the origin.[1 mark]
  6. 14(b)(iii)Write down the 2x1 matrix, T, which represents a translation of -3 units parallel to the x-axis and 5 units parallel to the y-axis.[1 mark]
  7. 14(b)(iv)Determine the coordinates of P' and P''.[1 mark]

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