Quelpr
3 marksMatrices and Systems of Linear Equations

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

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.

Reduce the augmented matrix to echelon form.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 6(a)(i)Write the augmented matrix of the system.[2 marks]
  2. 6(a)(iii)Deduce the value of k for which the system is consistent.[2 marks]
  3. 6(a)(iv)Find ALL solutions corresponding to the value of k obtained in (iii) above.[4 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]

More practice: the rest of this paper · more Matrices and Systems of Linear Equations questions · all CAPE Pure Mathematics Unit 2 past papers