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Year 12 Specialist (Unit 3 & 4) Applications of matrices

Inverses and determinants for 2×2 matrices andapplications to transformations.

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Questions
Question 1
162909

For the matrix \( A = \begin{bmatrix} 5 & 4 \\ 3 & -1 \end{bmatrix} \), find:
i) \(\operatorname{det}(A)\)
ii) \(A^{-1}\)

i) \(-17\)
ii) \(\frac{1}{17}\left[\begin{array}{cc}
1 & 4 \\
3 & -5
\end{array}\right]\)

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