Compute det[1 2 3; 4 5 6; 7 8 9] and decide what it says about the rows.

0: the third row is a combination of the other two

Exercise · ZW-DETERMINANT-010 · ★★★ Advanced

Compute \(\det\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}\) and decide what it says about the rows.

Choose one option.

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Row 3 = 2·(row 2) − (row 1), so the determinant is \(0\). With Sarrus: \(45+84+96-105-48-72=0\).

The determinant of a square matrix is a number that measures how much the linear transformation it defines scales volumes.

\[\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bc\]