For matrix A, with Aᵢⱼ the cofactor of aᵢⱼ, what is a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃?

Determinants, Adjoint & Inverse · Question 45 of 87

Question 45

HardOriginal question

For $A = \begin{bmatrix}2 & -1 & 3 \\ 0 & 4 & 1 \\ 5 & 2 & -2\end{bmatrix}$ , with $A_{ij}$ the cofactor of $a_{ij}$ , what is $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$ ?

-85

Correct answerYour answer

0

Correct answerYour answer

1

Correct answerYour answer

85

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

These are the elements of row 1 times the cofactors of row 2.
Elements of one row times the cofactors of a different row always add up to 0; only matching rows give $|A|$ .

Worth noting

$-85$ is $|A|$ , which needs the cofactors of the same row.

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

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