What is det[0, a, - b; - a, 0, c; b, - c, 0]?

Determinants, Adjoint & Inverse · Question 14 of 87

Question 14

MediumOriginal question

What is $\begin{vmatrix}0 & a & - b \\ - a & 0 & c \\ b & - c & 0\end{vmatrix}$ ?

0

Correct answerYour answer

2 a b c

Correct answerYour answer

- 2 a b c

Correct answerYour answer

a^{2} + b^{2} + c^{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Expand along row 1: $0 - a(0 - bc) + (-b)(ac - 0) = abc - abc$ .
So the value is 0. This matrix is skew-symmetric of order 3, and every skew-symmetric matrix of odd order has determinant 0.

Worth noting

$2abc$ gives the term $-b(ac)$ a plus sign; the two $abc$ terms cancel.

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

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