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Question 1 (40 points): Projection onto col/l with ATA = I _2~ 3% 2 Consider the matrix A : Dmlbmlm K N: H ll lI and the vector 3: ( ) (see Unit 2, slide 19). a) Prove that h colA, that is, that 3 cannot be expressed as a linear combination of the columns of A. (10p) o b) Check that F = E projw,A( ) is orthogonal to each column of A (which implies that 'F' is orthogonal to col/l). (10p) c) Check that the sum of the projections of 5 onto the directions given by the columns of A is equal to its projection onto colA. (20p)