Linear AlgebraCan you help with these questions that is attached, #15, #18 & #19?? 15. Define four polynomials as follows: P1(t) =t3 - 2t2 + 1, P2(t)2t³ + 3t + 2, P4(t)subset of {p1, P2, P3, P4} that is a basis forthe span of this set of four polynomials.Explain.2t² + t, P3(t)4t2 +4t. Find a L(p) = p". What are Ker(L), Range(L),be defined byP, be defined by18. Let L : P.L(p) =and Dim (Domain(L))?->19. Let u = (1, 1), v = (3, -2), w = (4, 3), andy = (-3,4). Let L be a linear map from R?to R? such that L(u)z = (7,5), what is L(z)?w and L(v) = y. If

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Answered: 15. Define four polynomials as follows:…

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

Can you help with these questions that is attached, #15, #18 & #19??

15. Define four polynomials as follows: P1(t) =
t3 - 2t2 + 1, P2(t)
2t³ + 3t + 2, P4(t)
subset of {p1, P2, P3, P4} that is a basis for
the span of this set of four polynomials.
Explain.
2t² + t, P3(t)
4t2 +4t. Find a

L(p) = p". What are Ker(L), Range(L),
be defined by
P, be defined by
18. Let L : P.
L(p) =
and Dim (Domain(L))?
->
19. Let u = (1, 1), v = (3, -2), w = (4, 3), and
y = (-3,4). Let L be a linear map from R?
to R? such that L(u)
z = (7,5), what is L(z)?
w and L(v) = y. If

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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