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