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In Exercises 21 and $22, A$ and $B$ are $n \times n$ matrices. Mark each statement True or False. Justify each answer.a. If $A$ is $3 \times 3,$ with columns $\mathbf{a}_{1}, \mathbf{a}_{2},$ and $\mathbf{a}_{3},$ then $\operatorname{det} A$ equals the volume of the parallelepiped determined by $\mathbf{a}_{1},$ $\mathbf{a}_{2}$ and $\mathbf{a}_{3}$ .b. $\operatorname{det} A^{T}=(-1)$ det $A$c. The multiplicity of a root $r$ of the characteristic equation of $A$ is called the algebraic multiplicity of $r$ as an eigen-value of $A .$d. A row replacement operation on $A$ does not change the eigenvalues.

a) Fb) Fc) Td) F

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 2

The Characteristic Equation

Vectors

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Okay, so a is false because this is just the absolute value to determine it. He is also false cause determinants of a is equal to the determinant of 80. We notice from my term. Uh, but see, it's joke. Murthy is false.

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