Q6. The set B = {1+t2, t+t, 1+2t+t2} is a basis for P2. Find the coordinate...
The set B = = {1-12 1-12.1-2-2) is a basis for P2. Find the coordinate vector of p(t) = 3+3+ - 32 relative to B. [Pls - (Simplify your answer.)
Let S = {t2.t-1,1} be an ordered basis for P2(t). If the vector v in P2(6) has the coordinate vector 2 3 with respect to S, then what is the vector v? Select one: O at2 + 2t +1 O b. +2 +1+1 O c. 12 + 2t - 1 O d. t2 + 2t
Question 2 (1 point) The set B below is a basis for P2. Find the coordinate vector of p(t) 3+t - 6t relative to B = {1-tt-t,2 – 2t+t} O 7 -3 o co 1 6 O 3 t 6t O 13 -10 Question 3 (2 points) Let A be the matrix defined below. -8 8 -8 1 -9 7 -7 7 4 3 A= 6 -9 4 9 -4 5 -5 5 6 -1 -7 -7 -7 0 Suppose...
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...
Let p, (t) 6+t, P2(t) =t-3t, p3 (t) = 1 +t-2t. Complete parts (a) and (b) below. Use coordinate vectors to show that these polynomials form a basis for P2. What are the coordinate vectors corresponding to p, p2, and pa? P- Place these coordinate vectors into the columns fa matrix A. What can be said about the matrix A? O A. The matrix A forms a basis for R3 by the Invertible Matrix Theorem because all square matrices are...
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
1 point) Determine whether each set Pi.P2 is a linearly independent set in P3s. Type "yes" or no for each answer. The polynomials Pi (t) = 1 + t2 and P2 () = 1-2 . The polynomials pi (t)-2t + t 2 and P2 (t) 1+· The polynomials p (t) -21-4t2 and P2 (t) 6t2-3.
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 for P2? Justify. If it is not a basis for P, then extend B to a basis for P2 Calculator is allowed b) Use the basis found in part (a) to find the coordinate vector of f--1-3x-5x2 Calculator is allowed 3. (6) Let B-(1-3r,x +2x2,1-3x-8x2,2+x-5x2) be the set of vectors in P a)...
Chapter Find the coordinate matrix of P3x3x-6 relative to the standard basis in P2 Chapter Find the coordinate matrix of P3x3x-6 relative to the standard basis in P2
Let α = {1 + 2t, t − t 2 , t + t 2} (a) Show that α is a basis for P2(R). (b) Let p(t) = 1 + 3t + t 2 . Find [p(t)]α. (c) Define the transformation T : P2(R) → P2(R) as T (p(t)) = p 0 (t) − p(t) i.e., the difference of p(t) and its first derivative. Determine whether this transformation is a linear transformation. (d) Find [T]α Problem 4. Let a =...