Evaluate det[1, 2, -1; 0, 3, 2; 4, 1, 5].

Determinants, Adjoint & Inverse · Question 21 of 87

Question 21

MediumOriginal question

Evaluate $\begin{vmatrix}1 & 2 & -1 \\ 0 & 3 & 2 \\ 4 & 1 & 5\end{vmatrix}$ .

-41

Correct answerYour answer

9

Correct answerYour answer

41

Correct answerYour answer

45

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Expand along column 1, which has a zero: $1 \cdot \begin{vmatrix} 3 & 2 \\ 1 & 5 \end{vmatrix} - 0 + 4 \cdot \begin{vmatrix} 2 & -1 \\ 3 & 2 \end{vmatrix}$ .
$= 1(15 - 2) + 4(4 + 3) = 13 + 28 = 41$ .

Worth noting

Along column 1 the signs are $+, -, +$ ; the third term keeps its $+$ .

Ten questions from Determinants, Adjoint & Inverse, at your own pace.

Ten questions from Determinants, Adjoint & Inverse, at your own pace.