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Consider a 2 × 2 matrix A with A² = A. a. If w is in the image of A, what is the relationship between w and Aw? b. What can you say about A if rank(A) = 2? What if rank(A) = 0? c. If rank(A) tion T (x) = Ax is the projection onto im(A) along ker(A). See Exercise 2.2.33. 1, show that the linear transforma-

Consider a 2 × 2 matrix A with A² = A. a. If w is in the image of A, what is the relationship between w and Aw? b. What can you say about A if rank(A) = 2? What if rank(A) = 0? c. If rank(A) tion T (x) = Ax is the projection onto im(A) along ker(A). See Exercise 2.2.33. 1, show that the linear transforma-

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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Please answer part C.

48. Consider a 2 × 2 matrix A with A2 = A. a. If w is in the image of A, what is the relationship between w and Aw? b. What can you say about A if rank(A) = 2? What if rank(A) = 0? c. If rank(A) = tion T (x) = A is the projection onto im(A) along 1, show that the linear transforma- ker(A). See Exercise 2.2.33.
Transcribed Image Text:48. Consider a 2 × 2 matrix A with A2 = A. a. If w is in the image of A, what is the relationship between w and Aw? b. What can you say about A if rank(A) = 2? What if rank(A) = 0? c. If rank(A) = tion T (x) = A is the projection onto im(A) along 1, show that the linear transforma- ker(A). See Exercise 2.2.33.
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