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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
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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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).
Transcribed Image Text: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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