MATH 235 Midterm: MATH 235 UMass Amherst practice-exam2-fall06
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Practice test 2: hints: (20 points) let ~v1 = and let ~v2. Let v be the subspace spanned by ~v1 and ~v2. Prove that ~v1 is not perpendicular to ~v2: (8 pts) Use gram-schmidt on {~v1, ~v2} to nd orthonormal basis {~u1, ~u2}. If we were able to nd a quadratic polynomial that went through all four points, then be a solution to a~x = ~b, where a b c. This has no solution, but we can nd the least squares solution by solving the normal equation for this linear system, The last step is to translate the solution back to a polynomial: (28 points) let v c be subspace spanned by {ex, xex, x2ex}. The dimension is the number of elements in a basis. B = (ex, xex, x2ex): (8 pts) Let d : v v be the linear transformation given by d(f ) = f .
