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Are the following statements true or false? If true, explain why. If false, provide a counter example. (a) Consider the equation (r, y, 2) = (1, 1, 1) + (a, b, c)s + (a², &², c²)t for s,t € R. It is not possible to find 3 sets of values for a, b and e such that each set makes this equation describe a different geometric object. (b) It is possible to have two matricies A and B such that AB exists, BA exists, and yet A+ B does not exist. (c) The is no 2 x 2 matrix M such that M² = M unless M is the identity matrix or the zero matrix.

Are the following statements true or false? If true, explain why. If false, provide a counter example. (a) Consider the equation (r, y, 2) = (1, 1, 1) + (a, b, c)s + (a², &², c²)t for s,t € R. It is not possible to find 3 sets of values for a, b and e such that each set makes this equation describe a different geometric object. (b) It is possible to have two matricies A and B such that AB exists, BA exists, and yet A+ B does not exist. (c) The is no 2 x 2 matrix M such that M² = M unless M is the identity matrix or the zero matrix.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Are the following statements true or false? If true, explain why. If false, provide a counter example. (a) Consider the equation (r, y, 2) = (1, 1, 1) + (a, b, c)s + (a², &², c²)t for s,t € R. It is not possible to find 3 sets of values for a, b and e such that each set makes this equation describe a different geometric object. (b) It is possible to have two matricies A and B such that AB exists, BA exists, and yet A+ B does not exist. (c) The is no 2 x 2 matrix M such that M² = M unless M is the identity matrix or the zero matrix.
Transcribed Image Text:Are the following statements true or false? If true, explain why. If false, provide a counter example. (a) Consider the equation (r, y, 2) = (1, 1, 1) + (a, b, c)s + (a², &², c²)t for s,t € R. It is not possible to find 3 sets of values for a, b and e such that each set makes this equation describe a different geometric object. (b) It is possible to have two matricies A and B such that AB exists, BA exists, and yet A+ B does not exist. (c) The is no 2 x 2 matrix M such that M² = M unless M is the identity matrix or the zero matrix.
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