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# LetA be anm X n matrix. (a) Prove thatA andA1A have the same null space. (b) Use the

ISBN: 9781449679545 435

## Solution for problem 41 Chapter 6.4

Linear Algebra with Applications | 8th Edition

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Linear Algebra with Applications | 8th Edition

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Problem 41

LetA be anm X n matrix. (a) Prove thatA andA1A have the same null space. (b) Use the rank/nullity theorem to prove that (A1A) is invertible if and only if rank{A) = n. (The relevance for us at this time is that pinv(A) = (A1At1A1 then exists if rank{A) = n.)

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Step 1 of 3

L3 - 2 3. Two basic triangles π/3 π/6 π/4 4. Unit circle (r =1 ,osi θ = y and cosθ = x) π/2 2π/3 π/3 3π/4 π/4 π/6 5π/6 π 0 7π/6 11π/6 5π/4 7π/4 4π/3 5π/3 3π/2 θ 0

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LetA be anm X n matrix. (a) Prove thatA andA1A have the same null space. (b) Use the