5.1 Pr 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 A = 1 1 2 0 1 Theorem 5.3 Let A be anm x n matrix. Then (a) (aA)+ = a-A*, if a # 0 is a scalar, (b) (A')* = (A+)', (c) (A*)+ = A, (d) A+ = A-1, if A is square and nonsingular, (e) (A'A)+ = A+A+' and (AA')+ = A+'A*, (f) (AA*)+ = AA+ and (A+A)+ = A* A, %3D %3D (h) At = (A'A)-'A' and A+A = In, if rank(A) = n, A 4(AA)-Land A4 (G) A+ = A', if the columns of A are orthogonal, that is, A'A = I,. mif remk(A) = m,
5.1 Pr 5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of [1 1 1 1 A = 1 1 2 0 1 Theorem 5.3 Let A be anm x n matrix. Then (a) (aA)+ = a-A*, if a # 0 is a scalar, (b) (A')* = (A+)', (c) (A*)+ = A, (d) A+ = A-1, if A is square and nonsingular, (e) (A'A)+ = A+A+' and (AA')+ = A+'A*, (f) (AA*)+ = AA+ and (A+A)+ = A* A, %3D %3D (h) At = (A'A)-'A' and A+A = In, if rank(A) = n, A 4(AA)-Land A4 (G) A+ = A', if the columns of A are orthogonal, that is, A'A = I,. mif remk(A) = m,
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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Transcribed Image Text:5.1 Prove results (a)-(u)
5.2 Use Theorem 5.3(h) to find the Moore-Penrose inverse of
[1
1
1
1
The
A =
0.
1
1
2
0.
1
Theorem 5.3 Let A be an m x n matrix. Then
(a) (aA)+ = a-1A+, if a # 0 is a scalar,
(b) (A')* = (A+)',
(c) (A*)+ = A,
(d) A+ = A-1, if A is square and nonsingular,
(e) (A'A)+ = A+A+' and (AA')+ = A+'A*,
(f) (AA+)+ = AA+ and (A+ A)+ = A* A,
(h) A+ = (A'A)-'A' and At A = In, if rank(A) = n,
44(A4)-Lend A4
(i) A+ = A', if the columns of A are orthogonal, that is, A'A = I.
%3D
|3D
%3D
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