Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0)...
Let T: R3 R3 be a linear transformation such that T(1,1,1) = (2,0,-1) T(0,-1,2)= (-3,2,-1) T(1,0,1) = (1,1,0) Find T(-2,1,0). a) (10,0,2) b)(3,-1,-1) c) (2,2,2) d) (-3,-2, -3) Your answer MacBook Air
3. Let T : R3 → R3 be a linear transformation which maps T(1,2,0) = (1,1,1) and T(2,0,1) = (1,-1,1) and T(0,0,1)- (1,0,0). Calculate the following (a) T(4.0,2) (b) T(3, 2,3) (c) T(a (5,0,4) for wbat ?
5. Let T: P2(R) R3 be a linear transformation such that T(1) = (-1,2, -3), T(1 + 3x) = (4,-5,6), and T(1 + x²) = (-7,8,-9). a. Show that {1,1 + 3x ,1 + x2} is a basis for P(R) (7pts) b. Compute T(-1+ 4x + 2x²). (3pts)
Let B (1,1, , (1,1,0), (2,0,0))} and = {(0,0,1), (0,2,3), (1,1,1)} be bases for R3. Find Pa and P Let B (1,1, , (1,1,0), (2,0,0))} and = {(0,0,1), (0,2,3), (1,1,1)} be bases for R3. Find Pa and P
1. Let F: R4-R3 be a linear transformation satisfying F(1,1,1,1) (0, 1,2), F(1,1,0, 1)(0, 0,2) F(0,1,0, 0) 1,0,0) F(1,1,0,0) (0,0,0), (a) Calculate F(x, y, z, w) (b) Calculate ker(F) and R(F)
Transformation T:R' -»R',T(x,y, z) = (x+y,x-z)nd v=< 1,-1,2 > 8. ar iven B <1,1,1>,< 1,0,1 ><-1,0,1>},B^ = {<1,1>,<1,0 >},and B, = {<1,0>,< 1,1>} B to Biand from B to B2 a) Find the Transition matrix from b) Find v],T[v];,7[v] c) Find v,and [v]p d) What did you conclude? Transformation T:R' -»R',T(x,y, z) = (x+y,x-z)nd v= 8. ar iven B ,},B^ = {,},and B, = {,} B to Biand from B to B2 a) Find the Transition matrix from b) Find...
Let T: R3 ? R3 be a linear transformation such that T(1, o, o)-(4,-1,2). TO, 1, o)-(,-2. 3), and To, o. 1)-a,-20·Find the indicated image.
Linear algebra, I need someone to tell me how to get T(1)=1,1,1 T(x)=-1,0,1 T(x^2)=1,0,1 T(x^3)=-1,0, 1 I don't have any clue to find this. please follwo the comment WHAT FORMULA SHOULD I PLUG IN WHEN I PLUG IN T(1), T(X)...... How about this: Problem 2. Let P3 = Span {1,2,22,23 , the vector space of polynomials with degree at most 3, and let T : P3 → R3 be the linear transformation given by T(p)p(0) 1000 1) Find the matrix...
(1 point) Let f:R → R'be the linear transformation defined by T 4 -5 51 f(T) = -1 2 - 5 . | -4 0 3 Let B = {(-2,-1, 1), (-2, -2,1),(-1,-1,0)}, C = {{-2, -1, 1), (2,0, -1),(-1,1,0)}, be two different bases for R3. Find the matrix f for f relative to the basis B in the domain and C in the codomain. IT 3
(20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in W? (b) Is the vector b (c) Find the solutionx to the least square problem for Ax = b. (d) What is the vector in W that best approximates b? (20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in W? (b) Is the vector b...