Let A be an m × n matrix. Use the steps below to show that a vector x in Rn satisfies Ax=0 if and only if ATAx =0. This will show that Nul A = Nul ATA. a. Show that if Ax =0, then ATAx =0 b. Suppose ATAx = 0. Explain why xTATAx =0, and use this to show that Ax =0.
Let A be an m × n matrix. Use the steps below to show that a vector x in Rn satisfies Ax=0 if and only if ATAx =0. This will show that Nul A = Nul ATA. a. Show that if Ax =0, then ATAx =0 b. Suppose ATAx = 0. Explain why xTATAx =0, and use this to show that Ax =0.
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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Let A be an m × n matrix. Use the steps below to show that a
a. Show that if Ax =0, then ATAx =0
b. Suppose ATAx = 0. Explain why xTATAx =0, and use this to show that Ax =0.
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