Question 5 of 58intermediate🔧 ApplyNumerical2 marks

Evaluate the determinants (i) ∣3−1−200−13−50∣\begin{vmatrix} 3 & -1 & -2 \\ 0 & 0 & -1 \\ 3 & -5 & 0 \end{vmatrix} (ii) ∣3−4511−2231∣\begin{vmatrix} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{vmatrix}

(i)
Answer

-12

(ii)
Answer

46

Explanation

For part (i), expanding along the second row is optimal since it contains two zeros, minimizing calculations. For part (ii), expanding along the first row using cofactors is straightforward. Both solutions follow the standard method of expanding determinants along a row or column using minors and cofactors as illustrated in Example 3 of the textbook context.