The linear tranformation L defined by L(p(x)) = -5p' - 15p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases E = {x3, x2, x, 1} and F = {x² +x+1, x + 1, 1} S = (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -7x³- 11x and g(x) = x² + 13. [L(p(x))]F = [L(g(x))]F= =

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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The linear tranformation L defined by
L(p(x)) = -5p' - 15p"
maps P4 into P3.
(a) Find the matrix representation of L with respect to the ordered bases
E = {x3, x2, x, 1} and F = {x² +x+1, x + 1, 1}
S =
(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -7x³- 11x and g(x) = x² + 13.
[L(p(x))]F
=
[L(g(x))]F=
=
Transcribed Image Text:The linear tranformation L defined by L(p(x)) = -5p' - 15p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases E = {x3, x2, x, 1} and F = {x² +x+1, x + 1, 1} S = (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -7x³- 11x and g(x) = x² + 13. [L(p(x))]F = [L(g(x))]F= =
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