Let X be an n x k matrix, and let y be an n x 1 vector. Select all of the following statements which must be true. O Ifn = k, then there does not exist any k x 1 vector b which solves the equation X™Xb=X"y. O If XTX has rank k, then there is a unique k x 1 vector b which solves the equation XTX6=X"y.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let X be an n x k matrix, and let y be an n x 1 vector. Select all of the following statements
which must be true.
If n = k, then there does not exist any k x 1 vector b which solves the equation X™Xb=X™y.
O If XTX has rank k, then there is a unique k x 1 vector b which solves the equation XTXb=XTy.
If n > k, then there is a unique k x 1 vector b which solves the equation XTXb=X"y.
O If X has rank n, then there is a unique k x 1 vector b which solves the equation XTX6=XTy.
There is a uniquek x 1 vector b which solves the equation XTX6=XTy.
Transcribed Image Text:Let X be an n x k matrix, and let y be an n x 1 vector. Select all of the following statements which must be true. If n = k, then there does not exist any k x 1 vector b which solves the equation X™Xb=X™y. O If XTX has rank k, then there is a unique k x 1 vector b which solves the equation XTXb=XTy. If n > k, then there is a unique k x 1 vector b which solves the equation XTXb=X"y. O If X has rank n, then there is a unique k x 1 vector b which solves the equation XTX6=XTy. There is a uniquek x 1 vector b which solves the equation XTX6=XTy.
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