Suppose T: M2 2¬P2 is a linear transformation whose action on a basis for M22 is as follows: -1 0 3 3 -1 -1 = 2x2 -x+2 T 0 -1 = - 12.x2 +6x-9 3 3 = -4x2+x+1 2x2 -x -1 0 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.
Suppose T: M2 2¬P2 is a linear transformation whose action on a basis for M22 is as follows: -1 0 3 3 -1 -1 = 2x2 -x+2 T 0 -1 = - 12.x2 +6x-9 3 3 = -4x2+x+1 2x2 -x -1 0 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.
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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Solution will look like this, Example: (a+b+c-3d)x^2+(a-b-c)x+(a+b+3d)

Transcribed Image Text:Suppose T: M2.2 P2 is a linear transformation whose action on a basis for M22 is as follows:
0 0
-1 0
T
= 2x2 -x+2 T
0 -1
3 3
= - 12x2 +6x-9 T
3 3
-1
|= 2x2 -x
-4x²+x+1 _T
X.
1 0
-1 0
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 'A' character to indicate an exponent, e.g. ax^2-bx+c.
a b
d
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