Further Mathematics · OCR H245 · Topic 4.03

Matrices

The language of matrices, matrix addition and multiplication, linear transformations, 3-D transformations, invariance, determinants, inverses and more.

  • 9 sub-topics
  • Taught in Year 12
  • 125 practice questions
  • 9 animated lessons
Practice questions (125) Lessons Worksheets coming soon All OCR Further Mathematics topics

What the specification says

Every sub-topic OCR can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 4.03aThe language of matricesY12
  2. 4.03b-cMatrix addition and multiplicationY12
  3. 4.03d-eLinear transformationsY12
  4. 4.03f3-D transformationsY12
  5. 4.03gInvarianceY12
  6. 4.03h-mDeterminantsY12
  7. 4.03n-qInversesY12
  8. 4.03r-sSolution of simultaneous equationsY12
  9. 4.03tIntersection of planesY12

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 125 questions in this topic, free, no account needed.

Matrices

Easy

Matrix multiplication · Year 12 · 4 marks

A\mathbf{A}=(1−312){}= \begin{pmatrix} 1 & -3 \\ 1 & 2 \end{pmatrix}, B\mathbf{B}=(441−2){}= \begin{pmatrix} 4 & 4 \\ 1 & -2 \end{pmatrix}.
  1. (a)
    Find AB.
    (2)
  2. (b)
    Find BA and comment.
    (2)
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Part (a)2 marks

  1. Row of A\mathbf{A} times column of B\mathbf{B} for each entry.
  2. (11060)\begin{pmatrix} 1 & 10 \\ 6 & 0 \end{pmatrix}

Part (b)2 marks

  1. (8−4−1−7)\begin{pmatrix} 8 & -4 \\ -1 & -7 \end{pmatrix}
  2. In general AB≠BAAB \ne BA: matrix multiplication is not commutative.

Total4

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  • B
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Matrices

Medium

Rotation matrix · Year 12 · 3 marks

  1. Write down the matrix for a rotation of 30° anticlockwise about the origin, and find the image of (2, 0).
    (3)
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  1. (cos⁡30∘−sin⁡30∘sin⁡30∘cos⁡30∘)\begin{pmatrix} \cos 30^\circ & -\sin 30^\circ \\ \sin 30^\circ & \cos 30^\circ \end{pmatrix}
  2. Multiply by the column vector.
  3. (1.73,1)(1.73, 1)

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Matrices

Hard

Singular matrices · Year 12 · 3 marks

(12a241012)\begin{pmatrix} 1 & 2 & a \\ 2 & 4 & 1 \\ 0 & 1 & 2 \end{pmatrix}
  1. Find the value of a for which the matrix is singular.
    (3)

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  1. Expand.det⁡\det=1(4(2)−1){}= 1(4(2) - 1)−2(2(2)−0){}- 2(2(2) - 0)+a(2−0){}+ a(2 - 0)
  2. =−1+2a= -1 + 2a
  3. Singular when det⁡=0\det = 0.a=12a = \tfrac{1}{2}

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