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AS 1 Pure Mathematics

Quick questions on Matrices: algebra, the 2x2 determinant and inverse, and matrices as transformations of the plane - CCEA A-Level Further Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is matrix algebra?
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For 2×22 \times 2 matrices the product is $(abcd)(efgh)=(ae+bgaf+bhce+dgcf+dh).\begin{pmatrix} a & b \\ c & d \end{pmatrix}\begin{pmatrix} e & f \\ g & h \end{pmatrix} = \begin{pmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{pmatrix}.$
What are matrices as transformations?
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A combined transformation is the product of the matrices, applied right to left: B\mathbf{B} then A\mathbf{A} is AB\mathbf{AB}.
What is q1?
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Find det⁡(4231)\det\begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix}. [1 mark]
What is q2?
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Write down the matrix for an enlargement, centre the origin, scale factor 33. [1 mark]
What is q3?
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Show that (2412)\begin{pmatrix} 2 & 4 \\ 1 & 2 \end{pmatrix} is singular. [2 marks]

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