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4 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2 · Question 6(a)(iv)

A system of equations is given by \begin{aligned} x + y + z &= 0 \\ 2x + y - z &= -1 \\ x + 2y + 4z &= k \end{aligned} where k is a real number.

Find ALL solutions corresponding to the value of k obtained in (iii) above.

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Other parts of this question

  1. 6(a)(i)Write the augmented matrix of the system.[2 marks]
  2. 6(a)(ii)Reduce the augmented matrix to echelon form.[3 marks]
  3. 6(a)(iii)Deduce the value of k for which the system is consistent.[2 marks]
  4. 6(b)(i)a)Find A^2.[4 marks]
  5. 6(b)(i)b)Find B = 3I + A - A^2.[4 marks]
  6. 6(b)(ii)Calculate AB.[4 marks]
  7. 6(b)(iii)Deduce the inverse, A^{-1}, of the matrix A.[2 marks]

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