linear algebra help pls 4. Let P2= {ao +ait+azt | ao, a1, a2 E R}. That is, P2 is the linear space of all polynomials of degree less than or equalto two. Let L: P2 P2 be the linear transformation defined byL(f(t)) = f(0) + S(3)t.For example, L(1+21 +3t) = (1+ 2(0) +3(0)2) + (1 + 2(3) + 3(3)) t =1+34t. Similarly, L(1) = 1+t and L(t) = 3t.(a) Find L(t2) =(b) Assume that L is a linear transformation and that A = {1,t, t2 is the standard basis for P2. Give the definitionof La and then find it.%3D(c) The set C = {1 – t2, 1 + t2, 1 +t + t2} is another basis for P2. Find the change of basis matrix P such that(L]e = P '(L]aP.

Let P2=a0+a1t+a2t2:a0,a1,a2∈ℝ and L:P2→P2 be a linear transformation defined by Lft=f0+f3t To find…

Answered: 4. Let P2 {ao +ait+azt | a0, a1, a2 E…

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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linear algebra help pls

4. Let P2= {ao +ait+azt | ao, a1, a2 E R}. That is, P2 is the linear space of all polynomials of degree less than or equal
to two. Let L: P2 P2 be the linear transformation defined by
L(f(t)) = f(0) + S(3)t.
For example, L(1+21 +3t) = (1+ 2(0) +3(0)2) + (1 + 2(3) + 3(3)) t =1+34t. Similarly, L(1) = 1+t and L(t) = 3t.
(a) Find L(t2) =
(b) Assume that L is a linear transformation and that A = {1,t, t2 is the standard basis for P2. Give the definition
of La and then find it.
%3D
(c) The set C = {1 – t2, 1 + t2, 1 +t + t2} is another basis for P2. Find the change of basis matrix P such that
(L]e = P '(L]aP.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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