Question

for the subspace of R4 consisting of 4. Use the Gram-Schmidt process to find an orthonormal basis all vectors of the form ſal a + b [b+c] 5. Use the Gram-Schmidt process to find an orthonormal basis of the column space of the matrix [1-1 1 67 2 -1 3 1 A=4 1 91 [3 2 8 5 6. (a) Use the Gram-Schmidt process to find an orthonormal basis S = (P1, P2, P3) for P2, the vector space of polynomials of degree at most two, with respect to the inner product g(t), r(t) = Sat)r(t) dt. (b) Check that your answer to (a) is correct by computing each inner product (P1, P2), (P1, P3), (P2, P3). (Hint: It is enough to check orthogonality of the basis you got before normalizing, and this is less messy.) (c) Let q(t) = 3t. Compute (g(t), pi(t)) for each i = 1, 2, 3 and use your computations to write down the coordinate vector qs of q with respect to S.

Answer 1

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