What is det[1, a, b; - a, 1, c; - b, - c, 1]?

Determinants, Adjoint & Inverse · Question 22 of 87

Question 22

HardOriginal question

What is $\begin{vmatrix}1 & a & b \\ - a & 1 & c \\ - b & - c & 1\end{vmatrix}$ ?

- a^{2} - b^{2} - c^{2} + 1

Correct answerYour answer

a^{2} + b^{2} + c^{2} + 1

Correct answerYour answer

a^{2} - 2 a b c + b^{2} + c^{2} + 1

Correct answerYour answer

1

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Worth noting

$1 + a^2 + b^2 + c^2 - 2abc$ keeps the $abc$ terms, but one comes with $-a$ and one with $+b$ , so they cancel.

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

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