Suppose T: M22-P2 is a linear transformation whose action on a basis for M22 is as follows: 1 1 = -6x²-4 T 2 2 0 -1 = -x2 -x-1 -3 -3 = 6x2 – 3x+3 T = -2x2 -2x-2 T 20 0 0 -3 -3 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 = 0 c d

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Math linear Algebra

Suppose T: M2.2 P2 is a linear transformation whose action on a basis for M2.2 is as follows:
0 0
-6x2-4 T
2 0
0 -1
x²-x-1
-3 -3
11
6х2-3х+3 т
2 2
—2х2-2х-2 Т
-3 -3
0 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
T
c d
Transcribed Image Text:Suppose T: M2.2 P2 is a linear transformation whose action on a basis for M2.2 is as follows: 0 0 -6x2-4 T 2 0 0 -1 x²-x-1 -3 -3 11 6х2-3х+3 т 2 2 —2х2-2х-2 Т -3 -3 0 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 T c d
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