Suppose T: M2,2→P2 is a linear transformation whose action on a basis for M2,2 is as follows: 01 1 0 0 -1 [9] 711]=x²+3x+2 1=1=2x²- 0 -1 -1 Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c. a b d = -2x²-2x+2 T = 0 = -2x²+4

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 29RE
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Suppose T: M2,2→P2 is a linear transformation whose action on a basis for M2,2 is as follows:
0
70
√1 0
0 1
0 -1
-1 -1
Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c.
= -2x²-2x+2 T
= 0
-2x²+4
= x²+3x+2 T
= 2x²-5
Transcribed Image Text:Suppose T: M2,2→P2 is a linear transformation whose action on a basis for M2,2 is as follows: 0 70 √1 0 0 1 0 -1 -1 -1 Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c. = -2x²-2x+2 T = 0 -2x²+4 = x²+3x+2 T = 2x²-5
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