Homepage › Solution manuals › Gilbert Strang › Introduction to Linear Algebra › Exercise 2.7.7

Introduction to Linear Algebra

Exercise 2.7.7

Answers

(a): False: $[\begin{matrix} 0 & A \\ A & 0 \end{matrix}]$ is symmetric only if $A = A^{T}$ .
(b): False: The transpose of $AB$ is $B^{T} A^{T} = BA .$ So ${(AB)}^{T} = AB$ needs $BA = AB$ .
(c): True: Invertible symmetric matrices have symmetric inverses! Easiest proof is to transpose $A A^{- 1} = I$ .
(d): True: ${(ABC)}^{T}$ is $C^{T} B^{T} A^{T} (= CBA$ for symmetric matrices $A, B$ , and $C)$ .

mathchakra

2021-12-20 21:28

Comments