20-2 100 0 120-2 00 0 0 1Q1 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) projectiononto 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.

Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Answered: 20-211 0 0 0. 1 Q1 Let A = 20-20 0 0 1…

20-211 0 0 0. 1 Q1 Let A = 20-20 0 0 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

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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Question

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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