following as True or False justifying youranswers:a) Let A = [1 0 k]and B =|-1 2 -1.If ABA" = 0, then k = 1.1b) If p(x) = x² - (a + d)x + (ad- bc) and A = then p(A) = 0.c) If A is a non-singular matrix, then (I + AB)-'A = A(I + BA)-1.|1 0%3Dx x0 1 11d)1 x 0 xN0.1 xe) The vector (5,8,9, –5) is a linear combination of the vectors (1,2,2,–1) and(4,9,9,-4).

Answered: Image /qna-images/answer/158e16e4-6125-403b-8bad-aff8ec61213a.jpg

justifying your answers: 10 2 a) Let A = [1 0 k]and B =-1 2 -1. If ABAT = 0, then k = 1. b) If p(x) = x² - (a + d)x + (ad – bc) and A then p(A) = 0. %3D %3D c) If A is a non-singular matrix, then (I + AB)-'A = A(I + BA)-1. 1 0

justifying your answers: 10 2 a) Let A = [1 0 k]and B =-1 2 -1. If ABAT = 0, then k = 1. b) If p(x) = x² - (a + d)x + (ad – bc) and A then p(A) = 0. %3D %3D c) If A is a non-singular matrix, then (I + AB)-'A = A(I + BA)-1. 1 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

following as True or False justifying your
answers:
a) Let A = [1 0 k]and B =|-1 2 -1.If ABA" = 0, then k = 1.
1
b) If p(x) = x² - (a + d)x + (ad- bc) and A = then p(A) = 0.
c) If A is a non-singular matrix, then (I + AB)-'A = A(I + BA)-1.
|1 0
%3D
x x
0 1 11
d)
1 x 0 x
N0.
1 x
e) The vector (5,8,9, –5) is a linear combination of the vectors (1,2,2,–1) and
(4,9,9,-4).

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