36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with...
12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal. 12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal.
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x – 2y) Submit Answer [-70.71 Points] DETAILS LARLINALG8 6.3.007. Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y, z) = (8x + y,7y - z), v = (0, 1, -1) T(v)
Find a matrix A that completely determines the function T(x, y) = (2y − 3x, x − 4y, 0, x). Determine if T is one-to-one and onto.
6. Let T: P, – P, be the linear operator defined as T(p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [7]s, the matrix for T relative to B.
10) Determine whether the matrix operator is invertible, if so, find its inverse. a)T(x, y) = (3x + 4y, 5x + 7y) b)T(x1, X2 X3) = (x; + 2x2 + 3x3, xz – X3, X; +3x2 + 2x3)
2. Suppose the linear operator L:R2 + R2 has matrix representation A = (Lee = (_} -). with respect to the basis E = [(1,1), (1, -1)7]. (a) Find B = [L], with respect to the basis F= |(1,0), (2, 1)T] .
12. Consider the linear operator from R² to R² defined by matrix B. (5%) and v= {f: (350-9"), both in the standand ordered basis. @ Show that vis a basis for R. Find matrix K to express the lineat operator in the basis v
9. The linear function f is defined by f(x,y) = (x + 2y, 5x - y). (a) (5 pts) If ū=(-1,2) and 7 =(3, 1), check that fü+v) = f(ū) + f(ū). (b) (10 pts) Find the standard matrix for f.
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
Consider the differential operator T:P3(R)→P3(R) given by T(p(x))=2p″(x)−2p′(x)−2p‴(x) Find an ordered basis F for P3(R) such that T acts like a shift operator with respect to F, i.e. M??(?) (1 point) Consider the differential operator T : P3(R) → P3(R) given by T(p(x)) = 2p"(x) — 2p'(x) – 2p"(x) 1 Find an ordered basis F for P3(R) such that T acts like a shift operator with respect to F, i.e. MF(T) = 0 0 0 0 0 0 0 0...