For matrix A, what is a₂₁A₂₁ + a₂₂A₂₂ + a₂₃A₂₃, where Aᵢⱼ is the cofactor of aᵢⱼ?

Determinants, Adjoint & Inverse · Question 40 of 87

Question 40

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

-21

Correct answerYour answer

-18

Correct answerYour answer

0

Correct answerYour answer

21

Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Elements of a row times their own cofactors add up to the determinant.
The cofactors of row 2 are $1$ , $-4$ and $-7$ , so the sum is $2(1) + (-3)(-4) + 5(-7) = -21$ .

Worth noting

0 is what elements of one row times the cofactors of a different row give.

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

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