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Suppose T: P3-M2,2 is an isomorphism whose action is defined by T(ax3 + bx²+cx+d) = b+c=2d b-2d a+b b+c-4d and that we have the ordered bases =√x³, x² B = 3 MDB(T): for P3 and M2,2 respectively. = X, 1 D= a) Find the matrix of T corresponding to the ordered bases B and D. 10 01 00 ¹ D- (18]. [8] · [8] [89] 0 00 10 000 000 000 b) Find the matrix of T-1 corresponding to the ordered bases D and B. 000 MBD(T¹)= 0 0 0 000 c) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants Use the character to indicate an exponent, e.g. ax^2-bx+c. T-[:] = 0

Suppose T: P3-M2,2 is an isomorphism whose action is defined by T(ax3 + bx²+cx+d) = b+c=2d b-2d a+b b+c-4d and that we have the ordered bases =√x³, x² B = 3 MDB(T): for P3 and M2,2 respectively. = X, 1 D= a) Find the matrix of T corresponding to the ordered bases B and D. 10 01 00 ¹ D- (18]. [8] · [8] [89] 0 00 10 000 000 000 b) Find the matrix of T-1 corresponding to the ordered bases D and B. 000 MBD(T¹)= 0 0 0 000 c) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants Use the character to indicate an exponent, e.g. ax^2-bx+c. T-[:] = 0

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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Suppose T: P3-M2,2 is an isomorphism whose action is defined by T(ax³ + bx²+cx+d)= b+c=2d b-2d a+b b+c-4d and that we have the ordered bases = 1x³, x² B = X, for P3 and M₂.2 respectively. MDB(T) a) Find the matrix of I corresponding to the ordered bases B and D. 000 000 000 10 01 00 ¹ D- [8] [8] [8] 8:] [0]. 1 = " 00 00 10 b) Find the matrix of I-1 corresponding to the ordered bases D and B. 000 MBD(T¹)= 0 0 0 000 T¹ 2²:0 = 0 r s c) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.
Transcribed Image Text:Suppose T: P3-M2,2 is an isomorphism whose action is defined by T(ax³ + bx²+cx+d)= b+c=2d b-2d a+b b+c-4d and that we have the ordered bases = 1x³, x² B = X, for P3 and M₂.2 respectively. MDB(T) a) Find the matrix of I corresponding to the ordered bases B and D. 000 000 000 10 01 00 ¹ D- [8] [8] [8] 8:] [0]. 1 = " 00 00 10 b) Find the matrix of I-1 corresponding to the ordered bases D and B. 000 MBD(T¹)= 0 0 0 000 T¹ 2²:0 = 0 r s c) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.
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