The trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \ 0 & 5 & 3 \…

Question

The trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \ 0 & 5 & 3 \ 4 & -2 & 7 \end{bmatrix}$ is:

Accepted Answer

C. $13$

Trace $= a_{11} + a_{22} + a_{33} = 1 + 5 + 7 = 13$. The trace is invariant under cyclic permutations: $\operatorname{tr}(AB) = \operatorname{tr}(BA)$, and under similarity: $\operatorname{tr}(P^{-1}AP) = \operatorname{tr}(A)$.

Answer

$0$

Answer

$7$

Answer

$19$

The trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & 5 & 3 \\ 4 & -2 & 7 \end{bmatrix}$ is: