Linear algebra: please solve q26 and 27 correctly and handwritten 26. In P2, let Q = {p₁(x), p2(x), P3 (x)}, whereP₁(x) = −1+ x + 2x², p₂(x) = x + 3x², andP3(x) = 1+2x+8x2. Use the basis B = {1, x, x²}to show that Q is a basis for P₂.27. Let Q be the basis for P₂ given in Exercise 26. Find[p(x)]o for p(x) = 1 + x + x².28. Let Q be the basis for P2 given in Exercise 26. Find[p(x)] for p(x) = ao + a₁x + a₂x².29. In the vector space V of (2 x 2) matrices, let

From given basis B of P2 let us prove Q also forms the basis of P2.

Answered: 26. In P2, let Q = {pi(x), P2(x),…

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: please solve q26 and 27 correctly and handwritten

26. In P2, let Q = {p₁(x), p2(x), P3 (x)}, where
P₁(x) = −1+ x + 2x², p₂(x) = x + 3x², and
P3(x) = 1+2x+8x2. Use the basis B = {1, x, x²}
to show that Q is a basis for P₂.
27. Let Q be the basis for P₂ given in Exercise 26. Find
[p(x)]o for p(x) = 1 + x + x².
28. Let Q be the basis for P2 given in Exercise 26. Find
[p(x)] for p(x) = ao + a₁x + a₂x².
29. In the vector space V of (2 x 2) matrices, let

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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