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Question 1 (40 points): Projection onto col A with ATA = I -2V2 5 Consider the matrix A = 3V2 and the vector b = 10 (see Unit 2, slide 19). V/2 2 a) Prove that be colA, that is, that b cannot be expressed as a linear combination of the columns of A. (10p) b) Check that F = b- projectA(b) is orthogonal to each column of A (which implies that F is orthogonal to col A). (10p) c) Check that the sum of the projections of b onto the directions given by the columns of A is equal to its projection onto col.A. (20p)