Question 2 (1 point) The set B below is a basis for P2. Find the coordinate...
Question 1 (1 point) Let A be the matrix defined below. -8 8 -8 1 -9 7 4 3 A= 7 6 -7 -9 4 9 5 5 -5 7 6 -7 -1 0 -7 -7 Suppose we know that ele 100 0 1 0 } RREFA= 10 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 Find a basis for the null space of A. O -87 6 5 O -9 9 -9 3...
Q6. The set B = {1+t2, t+t, 1+2t+t2} is a basis for P2. Find the coordinate vector of p(t) = 3+t-6t2 relative to B.
Question 3 (2 points) Let A be the matrix defined below. 8 8 -8 1 -9 7 7 4. 3 -7 -9 A= 6 4 9 -4 5 -5 5 6 -1 7 7 -7 -7 0 Suppose we know that 1 0 5 0 0 1 2 3 0 1 3 RREFA= 0 0 0 1 - 1 0 0 0 0 0 0 0 0 0 0 Find the dimension of the null space of A.
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 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...
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 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
Exercise 2 Let B= (Po, P1, P2) be the standard basis for P2 and B= (91,92,93) where: 91 = 1+2,92 = x+r2 and 43 = 2 + x + x2 1. Show that S is a basis for P2. 2. Find the transition matrix PsB 3. Find the transition matrix PB-5 4. Let u=3+ 2.c + 2.ra. Deduce the coordinate vector for u relative to S.
QUESTION 10 Find a set of parametric equations of the line through the points (-7, 6, 3) and (-5, 12, 10). a.x=-7+6t, z = 6+7t, y = 3+5t b.x=-7+2t, y = 6 + 6t, 2 = 3 + 7t C. X=-7+60, y = 6+7t, z = 3+5t d.x=-7-20, y = 6+6t, 2 = 3-7 e.x=-7+2t, y = -6+6t, 2 – 3+7t
Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate matrix of x relative to the standard basis. B = {(1, 0, 1), (1, 1, 0), (0, 1, 1)), 2 [x] = 3 3 [x]s = 5 11 4