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Matrices and Linear Spaces

Quick questions on Matrix operations and determinants explained: H2 Further Mathematics

6short 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 the determinant of a 2x2 matrix?
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For A=(abcd)\mathbf{A} = \begin{pmatrix} a & b \\ c & d \end{pmatrix},
What is wrong dimension check?
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AB\mathbf{AB} exists only if the columns of A\mathbf{A} match the rows of B\mathbf{B}; check before multiplying.
What are cofactor sign slips?
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The middle term of a first-row 3×33\times3 expansion carries a minus sign; the checkerboard pattern is easy to drop.
What is q1?
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Compute det⁡(5234)\det\begin{pmatrix} 5 & 2 \\ 3 & 4 \end{pmatrix}. [1 mark]
What is q2?
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State whether AB=BA\mathbf{AB} = \mathbf{BA} holds for general matrices and why. [1 mark]
What is q3?
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What does det⁡A=0\det\mathbf{A} = 0 tell you about A\mathbf{A}? [2 marks]

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