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Matrices and Linear Spaces

Quick questions on Inverse matrices and linear systems explained: H2 Further Mathematics

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 the 3x3 inverse?
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In practice the graphing calculator computes a numerical inverse, but the method must be shown when a question asks for it.
What is solving a system by the inverse?
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A system of nn equations in nn unknowns is Ax=b\mathbf{Ax} = \mathbf{b}. If A\mathbf{A} is invertible, the unique solution is
What is q1?
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State the condition for a square matrix to be invertible. [1 mark]
What is q2?
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Write the inverse of (2013)\begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}. [2 marks]
What is q3?
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A 3×33\times3 system has det⁡A=0\det\mathbf{A} = 0 and reduces to a row (0 0 0∣4)(0\ 0\ 0 \mid 4). What can you conclude? [1 mark]

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