1 1 1 1 1 1 0 2 0 1 2 -1 5 3 6 4. Consider A = 01 -1 0-1 -1 2 -4 1 -2 with a corresponding rref (A) = 00 0 1 1 4 -2 10 9 15 00 0 0 0 • State a basis for the column space of A. . Choose one of the columns from A not selected as part of the basis and show how it is a linear combination of your basis.

Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).

Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..