Matrices & Determinants (Standard)

Matrices & Determinants: core idea

• 1. Eigenvalues of $\begin{pmatrix}2&0\\0&3\end{pmatrix}$: product?

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• 2. Det after row swap of $\begin{pmatrix}1&2\\3&4\end{pmatrix}$?

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• 3. Rank of $I_3$?

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• 4. $\begin{pmatrix}1&1\\0&1\end{pmatrix}\begin{pmatrix}1&0\\1&1\end{pmatrix}$: bottom-left?

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• 5. Char poly of $\begin{pmatrix}0&1\\0&0\end{pmatrix}$: constant term?

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• 6. Triangular $\begin{pmatrix}2&3\\0&4\end{pmatrix}$ det?

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• 7. Solve $\begin{pmatrix}1&1\\0&1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}3\\2\end{pmatrix}$: $x$?

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• 8. Adjugate of $\begin{pmatrix}a&b\\c&d\end{pmatrix}$ top-left?

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• 9. If det $A=5$, det $(2A)$ for $2\times2$?

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