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2 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2 · Question 5(c)(ii)

Given the matrices A = \begin{pmatrix} 1 & -1 & 1 \\ 1 & -2 & 4 \\ 1 & 3 & 9 \end{pmatrix}, B = \begin{pmatrix} 30 & -12 & 2 \\ 5 & -8 & 3 \\ -5 & 4 & 1 \end{pmatrix}.

Hence, deduce the inverse, A^{-1}, of the matrix A.

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Other parts of this question

  1. 5(a)(i)Given that P(A \cup B) = 0.7, calculate P(A \text{ only}).[3 marks]
  2. 5(a)(ii)Hence, determine whether events A and B are independent. Justify your answer.[2 marks]
  3. 5(b)(i)Represent the outcomes of the draws and their corresponding probabilities on a tree diagram.[4 marks]
  4. 5(b)(ii)Determine the probability that the second ball drawn is white.[3 marks]
  5. 5(c)(i)Show that AB = 20I.[5 marks]
  6. 5(c)(iii)Hence, or otherwise, solve the system of linear equations given by: \begin{aligned} x - y + z &= 1 \\ x - 2y + 4z &= 5 \\ x + 3y + 9z &= 25 \end{aligned}[6 marks]

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