Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for...
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2. a) Find the matrix of T with respect to a, (T): b) Let 3 be the basis { 1 -1}. Find (T18 c) Find (7)
2 Problem 6: (12.5 points) Consider the basis B-( | , I) of R2. a) Find the B-coordinate vector [vB of v - (4,5) b) Find the change of coordinates matrix from the standard basis coordinates to the coordinates relative to the basis B
Let T:R2 → R2 be the linear transformation that first reflects points through the x-axis and then then reflects points through the line y = -x. Find the standard matrix A for T.
Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure, and draw onto it the image T(w) as accurately as possible. (Hint: First try writing w as a linear combination of u and v.) TV (u) Problem 2. Let u = | and v Suppose T : R2 + R2 is a linear transformation with 6 1 3) Tu = T(u) = -3 and T(v)...
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
subject: Linear Algebra if someone could answer and explain why the answers are correct that would be much appreciated. Thanks in advance!! Exercises 1. The set P2 of polynomials of degree less than or equal to two is a vector space under polyno- mial addition and scalar multiplication by real numbers. (a) (5 points) Show that the set A = {1, 2, 22) is a basis for P2. (b) (2 points) Find the coordinate vector of an arbitrary polynomial of...
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B = (? =-3e1 + 2e, v2 = 2e1-6). Show that B is a basis of T. Now suppose that a linear mapping f : T T is represented with respect to 8(2) by the matrix oSe 4 6' Find the matrix B that represents f with respect to B.
3. (6 points/2 each) Let T:R2 + R2. State why T is not linear. (a) T(C1, C2) = (1, 1). (b) T(1, 2) = ( 1,). (c) T(x1, x2) = (1 + x1, x2).
Problem 6 A bilinear pairing on R2 is given on basis vectors by <ei, ei >= 13; <ei, e2 >=< e2, ej >= 7; <e2,e2 >= 26 a) [3 pts) Find the matrix representation of the pairing. b) (4 pts) Explain why the bilinear pairing defines an inner product. c) [3 pts) If v = [5 – 3]T, find a non-zero vector w with < v, w >= 0