Can you help me? This is linear algebra.
3. (6) Let B-(1-3r,x +2x2,1-3x-8x2,2+x-5x2) be the set of vectors in P a) Is the set B a basis fo...
Let B be the standard basis of the space P2 of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. 1-3t+ 2t?, - 4 + 9t-22, -1 + 412, + 3t - 6t2 Does the set of polynomials span P2? O A. Yes, since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between...
Prob. 4 (12.5 pts) The set of vectors S = {p1.p2.p3 } may be a basis for P2 p1 = 1 + x + x2 p2 = x + x2 p = x² a) Verify that this is the case. b) If it is a basis, find the coordinate vector of b relative to S. b = 7 - x + 2 x2
Let H={p() : p()= a + b + cf*: a,b,cer} (a)(3 marks) Show that H is a subspace of P3. (b) Let P1, P2, P3 be polynomials in H, such that Py(t) = 2, P2(t) = 1 +38P3(0)= -1-t-Use coordinate vectors in each of the following and justify your answer each part (1) (5 marks) Verify that {P1, P2, P3} form a linearly independent set in P3- (11) (2 marks) Verify that {P1, P2, P3} does not span P3. (111)...
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where pl :=1-x: p2 := x-x: p3 := 1+x: a Use the definition of coordinate vector to find the polynomial p4 in P, the vector of coordinates of which in the basis B is c4=(2,2,-2). b. Find the transition matrix StoB from the standard basis in P, to the basis B. What are the coordinates of the three standard coordinate vectors of the basis Sin...
Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be added to the set S to form a basis for P2? (i) 2 + 3x − 6x2 (ii) 4 + 3x − 16x2 (iii) 9 + 15x − 21x2 (A) all of them (B) (i) and (ii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) none of them (F) (i) only (G) (ii) only (H) (iii) only
Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be added to the set S to form a basis for P2? (i) 2 + 3x − 6x2 (ii) 4 + 3x − 16x2 (iii) 9 + 15x − 21x2 (A) all of them (B) (i) and (ii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) none of them (F) (i) only (G) (ii) only (H) (iii) only
, A is a linear transformation that maps vectors x in 975 into vectors Let A= 0 -2 1 b in R2 Consider the set of all possible vectors b-Ax, where x is of unit length. What is the longest vector b in this set, and what unit length vector x is used to obtain it? You can use Matlab to save time with the computations, but please justify your answer. , A is a linear transformation that maps vectors...
I am not sure where to start on this linear algebra question. The set of vectors for part a is these ones: 216 131 6. (a) [2] Is the set of vectors in Question 5 (b) a spanning set for R3? (b) [5] Let 01 U2 and vz Find (with justification) a vector w R4 such that w¢ Span何,v2, v3} (c) [3 In (b), is the set {oi,T2, T, a basis for R4? Justify your answer.
(1 point) Consider the ordered bases B = {-(7 + 3x), –(2+ x)} and C = {2,3 + x} for the vector space P2. a. Find the transition matrix from C to the standard ordered basis E = {1,x}. TE = b. Find the transition matrix from B to E. Te = c. Find the transition matrix from E to B. 100 TB = d. Find the transition matrix from C to B. TB = 11. !!! e. Find the...
Both Problems (1 pt) Consider the basis B of Ra consisting of vectors and Find x in R- whose coordinate vector relative to the basis B is [x]] = X = [-121 (1 pt) The set B = 3 | } is a basis for R2. 12 Find the coordinates of the vector x = relative to the basis B: [x]B =