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5а-7 -10a + 47 -10a + 41 2a – 1 -4a + 17 Let M(a) = -a + 2 2а + 8 2а -4 -4a + 14 (a) Find all values of a for which M(a) has some 2-dimensional eigenspace (for some eigenvalue). You might find it useful to know that 3 is an eigenvalue of M(a) for all values of a. (b) For each value that you find in (a), find a matrix P for which P-M(a)P = D, where D is diagonal.

5а-7 -10a + 47 -10a + 41 2a – 1 -4a + 17 Let M(a) = -a + 2 2а + 8 2а -4 -4a + 14 (a) Find all values of a for which M(a) has some 2-dimensional eigenspace (for some eigenvalue). You might find it useful to know that 3 is an eigenvalue of M(a) for all values of a. (b) For each value that you find in (a), find a matrix P for which P-M(a)P = D, where D is diagonal.

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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Problem 2 5a – 7 -10a + 47 -10a + 41 Let M(a) = -a + 2 2a + 8 2a – 1 2а-4 -4a + 14 -4a + 17 (a) Find all values of a for which M(a) has some 2-dimensional eigenspace (for some eigenvalue). You might find it useful to know that 3 is an eigenvalue of M(a) for all values of a. (b) For each value that you find in (a), find a matrix P for which P- M(a)P = D, where D is diagonal. (c) Find all values of a for which M(a) is diagonalizable.
Transcribed Image Text:Problem 2 5a – 7 -10a + 47 -10a + 41 Let M(a) = -a + 2 2a + 8 2a – 1 2а-4 -4a + 14 -4a + 17 (a) Find all values of a for which M(a) has some 2-dimensional eigenspace (for some eigenvalue). You might find it useful to know that 3 is an eigenvalue of M(a) for all values of a. (b) For each value that you find in (a), find a matrix P for which P- M(a)P = D, where D is diagonal. (c) Find all values of a for which M(a) is diagonalizable.
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