alleryThe trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & 5 & 3 \\ 4 & -2 & 7 \end{bmatrix}$ is:
A$0$
B$7$
C$13$
D$19$
Answer & Solution
Correct 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: $\operatorname{tr}(P^{-1}AP) = \operatorname{tr}(A)$.
Keep practising Unit 1B2: Algebraic Limits and Continuity
Browse all Unit 1B2: Algebraic Limits and Continuity questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
The decimal expansion of $\dfrac{257}{2^3 \cdot 5^4}$ terminates after how many decimal plThe product of the HCF and LCM of 6 and 20 is:Which of the following is an irrational number?The remainder when $2^{100}$ is divided by 7 isHow many positive integers less than 1000 are divisible by neither 2 nor 5?The HCF of two consecutive positive integers isIf $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(The smallest positive integer that is divisible by every integer from 1 to 10 is