Exercise 1.1.22

Question

Show that this formula $(* *)$ (\href{./exercise_1-1-21}{Exercise 1.1.21}) breaks down if $\left[\begin{array}{l}b \ d\end{array}ight]=m\left[\begin{array}{l}a \ c\end{array}ight]:$ dependent columns.

Neil Z. · Accepted Answer

If we have
$$\begin{bmatrix}b\d\end{bmatrix}=m\begin{bmatrix}a\c\end{bmatrix},$$
then $ad-bc = amc - mac = 0$, i.e. the inversion of $2\times 2$ matrix doesn't
exist.

Exercise 1.1.22

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Exercise 1.1.22

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