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Suppose A is an mxn matrix of real numbers and x in an nx1 column vector. a.)...

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Advance Math

Suppose A is an mxn matrix of real numbers andx in an nx1 column vector.

a.) suppose Ax=0. Show thatATAx=0.

b.)Suppose ATAx=0.show Ax=0.

c.) by part a and b, we can conclude that Nul(A) =Nul(ATA), and thus dim(Nul A) =dim(Nul(ATA)), and thus nullity(A) =nullity(ATA). prove the columns of A are linearlyindependent iff ATA is invertible.

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