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...
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) Find T (2,-1,1). a) (10,0,2) b) (3,-2-1) c)(2,2,2) d) (-3,-2, -3)
Can someone please help? Question 2. Let B = {(1,-1,1),(-1,1,1)} and C = {(1,-1,0),(0,0,1)} be subsets of R3 (a) Show that both the sets B and C are linearly independent sets of vectors with span B = spanc (12 marks] (b) Assuming the usual left to right ordering, find the transition matrix PB- [2 marks] (c) Given a basis D of R?, find the transition matrix PB-D given Pc+b = (32) [3 marks (d) Use the transition matrix PC-D in...
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 ?
2. (4) Let W = span{(1,1,1), (-1,1,0)). Let v = (1,-1,2). Find the decomposition v = w; + W2, where we W and W, EW+.
What is the subspace of R3 spanned by (1,1,1) and (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
(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...
= Problem 2: Let S {ei, C2, C3} denote the standard basis of R3 and let B = {(1,0,0)*, (1,1,0), (1,1,1)t}. Find the matrices for the change of basis from S to B and its inverse. That is find Ibs and Isb
Question 2. Let B- (1,-1,1).(-1,1,1) and C(1,-1,0), (0,0, 1)) be subsets of R3 (a) Show that both the sets B and C are hnearly independent sets of vectors with spanB - 12 marks 2 marks spanC (b) Assuming the usual left to right ordering, find the transition matrix PB-C (c) Given a basıs D of R2, find the transition matrux Ps-D given 2 1 Pc.D 3 2 3 marks (d) Use the transition matrix Pc-.D in (c) to find D...
5. (10pts) Let B (v1 (1,1,0), v2 (1,0,-1). v3 (0,1,-1)) be a basis of R3 Using the Gram-Schmidt process, find an orthogonal basis of R3. (You don't have to normalize the vectors.)