University:
California State University, Northridge
Course:
MATH 462 | Advanced Linear Algebra
Academic year:

2014
Views:

310

Pages:

2
Author:

Tebankamaf7y

MATH 462, Quiz 5 SoM1or1<.t, Name: (print) _________________ Each problem is worth 2 points. Show all your work. 1. A matrix A E 111nxn (C) is skew-symmetric if A T = -A. (a) Prove that if A is skew symmetric and n is odd then A is not invertible. (b) Give an example of an invertible skew-symmetric matrix in the case when n is even. A T==-A ,ck-t AT :c t':kt (-A) rUS£. �- c1 det(A) =tr/' d.et(A) rr"7!J ,'I' ()✓o r 1f n cktfA)� I_J - det(A) A 1:S '},,,0./ (1.1. vevtr'tf!4_. n ) :=; 2- A-�(!,:) 2olet(A)= 0 0 :.-c > ol.e t (,4) � ..:; > -1;.., �� 1/ f,y� �<:_ (olet (t1) � I ) 2. Let A, B E Mn x n (lF) be such that AB = -BA. Prove that if n is odd, and IF is not a flield of characteristic two, then A or B is not invertible.

Algebra, Quiz 5, Solutions

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