UNDERSTANDING ALGEBRA homework help (Page 3985-3987) - (e Compare and contrast your results from parts(b and(d 4 Find the matrix for d dx acting on the

# UNDERSTANDING ALGEBRA homework help (Page 3985-3987) - (e...

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(e) Compare and contrast your results from parts (b) and (d). 4. Find the “matrix” for d dx acting on the vector space of all power series in the ordered basis (1, x, x2 , x3 , ...). Use this matrix to find all power series solutions to the differential equation d dx f(x) = x. Hint: your “matrix” may not have finite size. 5. Find the matrix for d 2 dx2 acting on {c1 cos(x) + c2 sin(x) | c1, c2 R} in the ordered basis (cos(x),sin(x)). 6. Find the matrix for d dx acting on {c1 cosh(x) + c2 sinh(x)|c1, c2 R} in the ordered basis (cosh(x),sinh(x)) and in the ordered basis (cosh(x) + sinh(x), cosh(x) − sinh(x)). 7. Let B = (1, x, x2 ) be an ordered basis for V = {a0 + a1x + a2x 2 | a0, a1, a2 R} , and let B0 = (x 3 , x2 , x, 1) be an ordered basis for W = {a0 + a1x + a2x 2 + a3x 3 | a0, a1,

• Spring '16
• mr.butcher

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