What dimension is P3 (the set of polynomials degree 3 or less)?Which of the following sets form a basis for P3?{2+ x°,32x, x,— 5, 2а + 3}--{3, – a°, x}-{1, 2x, – 3x², 2æ³}V {2x², æ, – 5, 2 + æ³}-– 5, 2 + x* }-O {2x², z, 0, æ*} What dimension is M2,2 (the set of 2x2 matrices)?Which of the following sets form a basis for M2.2?[1 04 2|}5 70 0- 21 00 01 00 20 00 021 0-|0 21 00 00 0}1 00 2ㅇ0 00 021 04 2[1 0°0 05 70 02

?The dimension of P3 is 4. Since dimension of P3 is 4, the basis contains exactly 4 element which…

Answered: What dimension is P3 (the set of…

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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Is this B?
21
1) Compute the characteristic polynomial of A. (2) Determine whether or not A is diagonalizable.
Which of the sets of polynomials is Linearly independent? O (1+X, 1-X} O (1, X, 0} O (1+X, 2+2X} O (1+X, 1+2X, 3} None of these
(a) Let V be R², and the set of all ordered pairs (x, y) of real numbers. Define an addition by (a, b) + (c,d) = (a + c, 1) for all (a, b) and (c,d) in V. Define a scalar multiplication by k · (a, b) = (ka, b) for all k E R and (a, b) in V. . Verify the following axioms: (i) k(u + v) = ku + kv (ii) u + (-u) = 0
True or FalseThe set {(0,0),(1,0),(2,0),(3,0),(4,0)} is a principal ideal of z5 x z3.
P(x)] B The set B = {− (2 + 4x²), x −6 − 12x², 2x – 4 – 12x²} is a basis for P₂. Find the coordinates of p(x) = 20 − 3x + 40x² relative to this basis:
A. Find the rank and nullity B. Find a basis for the column space C. Find a basis for the nullspace
Let f=z" + an-12¹-1 + ... + a₁ € C[z] be a polynomial of degree n ≥ 1. Which of the factorisations below must exist? Select one or more: a. f=(z-C₁)(z-C₂)(z- Cn), where C₁, ..., Cn are complex numbers b. f= (z-C₁)(z-C₂)(z-Cn), where C₁, . ...., Cn are different complex numbers c. f=g₁(z) gk(z), where g₁, . ...., 9k € C[z] each have exactly one root, and all these roots are different d. f = (z² + r₁Z+S₁)... (z² + rkz + Sk), where r₁, ..., rk and S₁, ..., Sk are real numbers e. f=g₁(z) gk(z), where g₁, , ..., 9k € C[z] each have exactly one root, and their degrees are all different
Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||p|, |la|l, and d(p, q) for the polynomials in P₂. p(x) = 1 -x + 4x², g(x) = x - x² (a) (p, q) (b) ||p|| (c) |||| (d) d(p, q)
Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||p||, ||9||, and d(p, q) for the polynomials in P2. p(x) = 4x + 3x2, g(x) = x - x² (a) (p, q) (b) ||P|| (c) |||| d(p, q) (d)

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What dimension is P3 (the set of polynomials degree 3 or less)? Which of the following sets form a basis for P3? {2 + x°, - 2x2, x, – 5, 2x + 3} O {3, - V {1, 2x, – 3x², 2æ³ } - M {2a², z, – 5, 2 + a*} O {2r", z, 0, z*} 5, 2 + x*}

What dimension is P3 (the set of polynomials degree 3 or less)? Which of the following sets form a basis for P3? {2 + x°, - 2x2, x, – 5, 2x + 3} O {3, - V {1, 2x, – 3x², 2æ³ } - M {2a², z, – 5, 2 + a} O {2r", z, 0, z} 5, 2 + x*}