True/False. For each statement, say whether it's true or false. Give a brief but rigorous justification(for example, this could be a counterexample or a quick argument using a theorem).(a) The set defined by y +x = 2 is a linear subspace of R2.(b) There exists a 4 x 5 matrix A such that dim(im A) = 1 and dim(ker A) = 3.1 0and0 10 1(c) The matricesare similar.(d) If u and uz are unit vectors in R" with u1 ü2, then the vectors u1 + uz and ủ1 – ủz areorthogonal.

Answered: Image /qna-images/answer/9afa426f-9422-442f-a8a4-dad1416c9e63.jpg

(a) The set defined by y + a = 2 is a linear subspace of R2. (b) There exists a 4 x 5 matrix A such that dim(im A) = 1 and dim(ker A) = 3. 1 0 0 1 and 1 0 (c) The matrices are similar. 0 1 (d) If ū and u2 are unit vectors in R" with u1 ū2, then the vectors u + uz and ū – üz are orthogonal.

(a) The set defined by y + a = 2 is a linear subspace of R2. (b) There exists a 4 x 5 matrix A such that dim(im A) = 1 and dim(ker A) = 3. 1 0 0 1 and 1 0 (c) The matrices are similar. 0 1 (d) If ū and u2 are unit vectors in R" with u1 ū2, then the vectors u + uz and ū – üz are orthogonal.

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

True/False. For each statement, say whether it's true or false. Give a brief but rigorous justification
(for example, this could be a counterexample or a quick argument using a theorem).
(a) The set defined by y +x = 2 is a linear subspace of R2.
(b) There exists a 4 x 5 matrix A such that dim(im A) = 1 and dim(ker A) = 3.
1 0
and
0 1
0 1
(c) The matrices
are similar.
(d) If u and uz are unit vectors in R" with u1 ü2, then the vectors u1 + uz and ủ1 – ủz are
orthogonal.

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