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A-LevelFurther MathematicsMatrices9231/12 · Oct/Nov 2018 · Q26 Marks

It is given that A= 2 3 1 0 -2 1 0 0 1

  1. (i)Find the eigenvalue of A corresponding to the eigenvector (1 0 0) [1]
  2. (ii)Write down the negative eigenvalue of A and find a corresponding eigenvector.[3]
  3. (iii)Find an eigenvalue and a corresponding eigenvector of the matrix A + A6.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [B1] Stated
  2. [B1] Stated
  3. [M1] Uses vector product (or equations) to find corresponding eigenvector.
  4. [A1] Accept any non-zero scalar multiple of (3 -4 0)
  5. [B1] An eigenvalue of_A + A⁶ is 2+2⁶ = 66, 62 or 2
  6. [B1] Corresponding eigenvector is (3 -4 0) or (-6 1 3) oe

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About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 6 marks.
Source
A-Level Further Mathematics, Oct/Nov 2018 Paper 1 Variant 2, question 2.

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