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(1) Let T : R4 → P4 be the linear transformation given by T ((a, b, c, d)) = (a + b + 3c + 5d) + (b + 2c + 3d)X + (3a – 4b – 5c – 6d)X² + dX3 where P4 is the vector space of polynomials of degree < 4 with real coefficients. Find the matrix representation B(T]A of T with respect to the ordered basis A of R4 and the ordered basis B of P4 where A = {(0,0, 1,0), (0,0, 1,1), (1,0, 1, 0), (1, 1, 1, 1)} and B = {X², X³, 1, X } .

(1) Let T : R4 → P4 be the linear transformation given by T ((a, b, c, d)) = (a + b + 3c + 5d) + (b + 2c + 3d)X + (3a – 4b – 5c – 6d)X² + dX3 where P4 is the vector space of polynomials of degree < 4 with real coefficients. Find the matrix representation B(T]A of T with respect to the ordered basis A of R4 and the ordered basis B of P4 where A = {(0,0, 1,0), (0,0, 1,1), (1,0, 1, 0), (1, 1, 1, 1)} and B = {X², X³, 1, X } .

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(1) Let T : R4 → P4 be the linear transformation given by T (а,b, с, d)) — (а +b+3с + 5d) + (b + 2с + 3d)х + (За — 4 — 5с — 6d) X? + dx3 where P4 is the vector space of polynomials of degree < 4 with real coefficients. Find the matrix representation B[TA of T with respect to the ordered basis A of R4 and the ordered basis B of P4 where A = {(0,0,1,0), (0,0, 1, 1), (1,0, 1,0), (1, 1, 1, 1)} B = {X², X³, 1, X }. and
Transcribed Image Text:(1) Let T : R4 → P4 be the linear transformation given by T (а,b, с, d)) — (а +b+3с + 5d) + (b + 2с + 3d)х + (За — 4 — 5с — 6d) X? + dx3 where P4 is the vector space of polynomials of degree < 4 with real coefficients. Find the matrix representation B[TA of T with respect to the ordered basis A of R4 and the ordered basis B of P4 where A = {(0,0,1,0), (0,0, 1, 1), (1,0, 1,0), (1, 1, 1, 1)} B = {X², X³, 1, X }. and
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