Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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