1. Mark each statement as true or False. Justify your answer. If true, cite a theorem or fact from class. If false, explain why by giving the correct answer or a counter example. (a) S c R°, is the set of all unit vectors. S is a subspace of R°. (b) If a 3 x 3 matrix A has eigen values 1,2, 3,then its determinant is 6. (c) The matrix A = 0 -2] preserves areas of parallelograms in R2. (d) If a m x n matrix A has rank < m, then the homogenous system Ar = 0 cannot have a trivial solution.
1. Mark each statement as true or False. Justify your answer. If true, cite a theorem or fact from class. If false, explain why by giving the correct answer or a counter example. (a) S c R°, is the set of all unit vectors. S is a subspace of R°. (b) If a 3 x 3 matrix A has eigen values 1,2, 3,then its determinant is 6. (c) The matrix A = 0 -2] preserves areas of parallelograms in R2. (d) If a m x n matrix A has rank < m, then the homogenous system Ar = 0 cannot have a trivial solution.
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
![1. Mark each statement as true or False. Justify your answer. If true, cite a theorem
or fact from class. If false, explain why by giving the correct answer or a counter
example.
(a) Sc R°, is the set of all unit vectors. S is a subspace of R®.
(b) If a 3 x 3 matrix A has eigen values 1,2,3,then its determinant is 6.
[o -2]
(c) The matrix A =
preserves areas of parallelograms in R2.
(d) If a m x n matrix A has rank <m, then the homogenous system Ar = 0 cannot
have a trivial solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd96e1686-f3c3-4fc7-a74c-9617ccb753ef%2F968949e0-02fd-4ba9-8304-82a280a830eb%2Fmywh43l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Mark each statement as true or False. Justify your answer. If true, cite a theorem
or fact from class. If false, explain why by giving the correct answer or a counter
example.
(a) Sc R°, is the set of all unit vectors. S is a subspace of R®.
(b) If a 3 x 3 matrix A has eigen values 1,2,3,then its determinant is 6.
[o -2]
(c) The matrix A =
preserves areas of parallelograms in R2.
(d) If a m x n matrix A has rank <m, then the homogenous system Ar = 0 cannot
have a trivial solution.
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