20-2 11 0. 0 0 20-2 0 0 0 Q1 Let A = 1 a) Is A invertible? Justify your answer. b) Find a basis for Col(A) and Null(A)? c) For V Col(A) find a basis for the orthogonal complement of V? %3D d) For V = Col(A) write down the matrix P representing the (orthogonal) projection onto V? e) Find the eigenvalues together with the corresponding eigenspaces. f) If it is possible decompose A as SDS- where D is a diagonal matrix.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
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please answer d,e and f. thank you!

20-2 1
00 0 1
20-2 0
0 0 0 1
Q1 Let A =
a) Is A invertible? Justify your answer.
b) Find a basis for Col(A) and Null(A)?
c) For V = Col(A) find a basis for the orthogonal complement of V?
d) For V = Col(A) write down the matrix P representing the (orthogonal) projection
onto V?
e) Find the eigenvalues together with the corresponding eigenspaces.
f) If it is possible decompose A as SDS- where D is a diagonal matrix.
Transcribed Image Text:20-2 1 00 0 1 20-2 0 0 0 0 1 Q1 Let A = a) Is A invertible? Justify your answer. b) Find a basis for Col(A) and Null(A)? c) For V = Col(A) find a basis for the orthogonal complement of V? d) For V = Col(A) write down the matrix P representing the (orthogonal) projection onto V? e) Find the eigenvalues together with the corresponding eigenspaces. f) If it is possible decompose A as SDS- where D is a diagonal matrix.
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