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3 marksCombined Transformations

CSEC Mathematics · January 2009 · Paper 2 · Question 14(b)(ii)

The diagram shows a triangle, ABC whose coordinates are stated. Triangle ABC undergoes two successive transformations, V followed by W, where V = ((2, 0), (0, 2)) and W = ((-1, 0), (0, 1)).

Determine the 2 x 2 matrix that represents the combined transformation of V followed by W.

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Other parts of this question

  1. 14(a)Calculate the matrix product 3AB.[3 marks]
  2. 14(b)(i)State the effect of V on triangle ABC.[2 marks]
  3. 14(b)(iii)Using your matrix in (b)(ii), determine the coordinates of the image of triangle ABC under this combined transformation.[3 marks]
  4. 14(c)(i)Write the following simultaneous equations in the form AX = B where A, X and B are matrices: 11x + 6y = 6 and 9x + 5y = 7.[2 marks]
  5. 14(c)(ii)Hence, write the solution for x and y as a product of two matrices.[2 marks]

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