please answer the question 2) (1 point) For each transformation below, determine a basis for (Range(T))...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T la +(-1) 6+2c +(-1)d - 1a + 2b + 0c + Od -3a + 56+ (-1) +0d 2a +(-2) b + 3c +0d] с d T-1 2) Let T(a + bx + cx+ dx?) = 1a + 2b + 1c +(-1)d la + 3b + 3c + Od 3a + 7b +6c+(-3) d 8a + 196 +16c+(-6) d 1-[]- 3) Let T 13a +(-17)...
For each transformation T and basis B and C, find the corresponding matrix representation M of T from basis B to basis C. 1) Let T6 = la + 2b + 4c 3a +86 + 16c la + 3b + 6c be a linear transformation. -2a +(-7) + (-14)c] с 1 Let B= 2 > -1 4 0 2 Let C = [11] [32] [] [1] The matrix M for transformation T from basis B to C would be: 2)...
please finish questions 1) and 2) thank you (1 point) For each space W, determine a basis for W! Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 1) Let W= la + 2b + 5c + Od 2a + 5b + 11c + 2d -5a +...
For each pair of transformations "T" and "T-1", find T(T-1(w)) and T-?(T()). Then use T or F to indicate if these transformations are inverses of one another. 1) Let T(a + bx + cx2 + dx3) = la +16+(-1)c+ld Da +(-1) b+ 1c +(-1)d la + 2b +(-2) c + 3d 0a + 0 + 0c + 1d and T-1 = 1a +06+1c +0d + (4a + (-4) 6+ (-5) c + 3d) x + (-3a +36 +30 + (-2)...
find a basis for the range and the rank of the given linear transformation and determine if it is onto. 1) T: R3[x]→R2[x] given by T(a+bx+cx2+dx3) = (a+2b+c) + (2a+5b+c+d)x + (2a+6b+d)x2. 2) G).r« 2 ,T(e3) T (e2) 3. Т:R4 M2x2(R) given by T(ei) 2 3 -G ) (G) 2 ,T(е) 4 3 1 G).r« 2 ,T(e3) T (e2) 3. Т:R4 M2x2(R) given by T(ei) 2 3 -G ) (G) 2 ,T(е) 4 3 1
18. Let T be the matrix transformation T -1 2 0 -1 2 2 -1 h 2 -3 k 4 a. What are the domain and codomain of T? b. Find the REF of [T]. Hint: You'll need the REF in some of the following questions. -1 -1 -1 -3 (REF of [7]= 0 2 2 4 is given here so that you can correctly answer the following 0 0 h – 2 k-6 questions.) c. Define the range of...
Please provide answer in neat handwriting. Thank you Let P2 be the vector space of all polynomials with degree at most 2, and B be the basis {1,T,T*). T(p(x))-p(kr); thus, Consider the linear operator T : P) → given by where k 0 is a parameter (a) Find the matrix Tg,b representing T in the basis B (b) Verify whether T is one-to-one and whether or not it is onto. (c) Find the eigenvalues and the corresponding eigenspaces of the...
Question 2 (1 point) The set B below is a basis for P2. Find the coordinate vector of p(t) 3+t - 6t relative to B = {1-tt-t,2 – 2t+t} O 7 -3 o co 1 6 O 3 t 6t O 13 -10 Question 3 (2 points) Let A be the matrix defined below. -8 8 -8 1 -9 7 -7 7 4 3 A= 6 -9 4 9 -4 5 -5 5 6 -1 -7 -7 -7 0 Suppose...
Can u please answer the question (G) 1. (15 marks total) Consider the real vector space (IR3, +,-) and let W be the subset of R3 consisting of all elements (z, y, z) of R3 for which z t y-z = 0. (Although you do not need to show this, W is a vector subspace of R3, and therefore is itsclf a rcal vector space.) Consider the following vectors in W V2 (0,2,2) V (0,0,0) (a) (2 marks) Determine whether...
Please answer the parts below, thank you. A) B) C) (1 point) If A and B are 6 x 9 matrices, and C is a 8 x 6 matrix, which of the following are defined? A. B - A B. CB + 2A C. B-C D. CB E. AB (1 point) Parameterize the solutions to the following linear equation, and write your answer in vector form. -8x + 4y - 7z = -4 2 Solution: y + S +t. 2...