Please help me find my error in finding a linear matrix!!!?
Given T(f(t) = integral from -2 to 6 f(t) dt from P4 to R with respect to the standard basis for P4 and R,
A = [ ____, _____, ______, ______]
I evaluated kt for k = 1,2,3,4 and came up with [8, 16, 24, 32] but only the first two entries are right.
Given T(f(t) = integral from -2 to 6 f(t) dt from P4 to R with respect to the standard basis for P4 and R,
A = [ ____, _____, ______, ______]
I evaluated kt for k = 1,2,3,4 and came up with [8, 16, 24, 32] but only the first two entries are right.
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The standard basis for P4 is {1, t, t², t^3, t^4}. So your matrix A should have 5 entries, and they should be the integrals of the basis elements. It's rather amusing that you actually get the correct values for 1 and t (namely 8 and 16).
6
∫ t² dt = 6^3/3 - (-2)^3/3 = 224/3.
-2
To get the last two, just integrate t^3 and t^4.
6
∫ t² dt = 6^3/3 - (-2)^3/3 = 224/3.
-2
To get the last two, just integrate t^3 and t^4.