1. Let T : P, → P, be defined by T (p(x)) = x²d²p. Find the matrix of T relative to the standard basis of P3. 2. Suppose that we are given the following information about a linear transformation 1 -10 Find, if possible. If not possible, state why. -HED a) T b) T -6 11 -14 =x²-3x, = x² + 2x+1, 3 18 =x-2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I am really struggling with this matrix problem because I don't understand how to do these two problems can you do this step by step using the matrix form so I can understand it 

1. Let T : P, → P, be defined by T (p(x)) = x² d
р
dx²
the standard basis of P3.
2. Suppose that we are given the following information about a linear transformation
0
6
0
0
Find, if possible. If not possible, state why.
-0
b) T
D
T
-6
11
-5
-14
= x³ - 3x,
Find the matrix of T relative to
x²+2x+1,
=x-2.
Transcribed Image Text:1. Let T : P, → P, be defined by T (p(x)) = x² d р dx² the standard basis of P3. 2. Suppose that we are given the following information about a linear transformation 0 6 0 0 Find, if possible. If not possible, state why. -0 b) T D T -6 11 -5 -14 = x³ - 3x, Find the matrix of T relative to x²+2x+1, =x-2.
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