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3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0,...
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator...
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator on R whose matrix representation with respect to the ordered basis . is a) Determine the transition matrix (change of basis matrix) from, v,to (1) (Draw the commutative triangle). 3 b) Find the matrix representation B, of L with respect to ,v} by USING the similarity relation
vectors pure and applied. exercise 6.4.2 OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with resp...
vectors pure and applied. exercise 6.4.2
OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with respect to some basis. Then β would have Proof Suppose t matrix representation D=(d, 0 say, with respect to that basis and ß2 would have matrix representation 2 (d2 0 with respect to that basis. However for all xj, so β-0 and β2...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
2. Suppose the linear operator L:R2 + R2 has matrix representation A = (Lee = (_}...
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] .
solution of question d (4 points) Consider the basis of R5 given by with b2 (2,-1,-5,-4,7), b3-(3, 2,-7,-5,9) b4 2,1,4,...
solution of question d
(4 points) Consider the basis of R5 given by with b2 (2,-1,-5,-4,7), b3-(3, 2,-7,-5,9) b4 2,1,4,4,-5) bs (-1,0,1,2,0) The MATLAB code to produce the basis vectors is given by b1 11,0-2-2.3], b2 -12-1.-5-4,7T, b3 13-2-7-5,91, b4 [-2,14.4-5T, b5 1-1,0,1,20 Let S denote the standard basis for R a Find the transition matrix P P,s PB,s b. Use the previous answer to calculate the coordinate matrix of the vector z ( 1,5, 4, 3, 3) with respect...
2. Let T be the linear operator on C2 defined by Tc? = (1 + ?,...
2. Let T be the linear operator on C2 defined by Tc? = (1 + ?, 2), Te,-(i, i). Using the standard inner product, find the matrix of T* in the standard ordered basis. Does T commute with T*?
Let x = [xı x2 x3], and let TER → R be the linear transformation defined...
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
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 operato...
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...
JO # 2. Let the linear operator K : C([0, 1]) + C([0, 1]) be defined...
JO # 2. Let the linear operator K : C([0, 1]) + C([0, 1]) be defined for each continuous real valued function f on [0, 1] by (Kf)(x) = 1 | tf(t) dt. a. Find a range of values for the parameter 1 for which the operator norm of K is strictly less than 1 with respect to the norm on C([0, 1]) given by Il gl. = sup{lg(t)| :te [0, 1]}. b. Describe an iterative process for solving (generating...
6. Let :P - P be the linear operator defined as (p(x)) - (5x), and let...
6. Let :P - P be the linear operator defined as (p(x)) - (5x), and let B = (1.x.x) be the standard basis for P2 a.) (5 points) Find the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x Determine (px)then find (p(x)) using (Tle from parta c.) (1 point) Check your answer to part b by evaluating T(x+6x) directly
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator on R whose matrix representation with respect to the ordered basis . is a) Determine the transition matrix (change of basis matrix) from, v,to (1) (Draw the commutative triangle). 3 b) Find the matrix representation B, of L with respect to ,v} by USING the similarity relation
vectors pure and applied. exercise 6.4.2
OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with respect to some basis. Then β would have Proof Suppose t matrix representation D=(d, 0 say, with respect to that basis and ß2 would have matrix representation 2 (d2 0 with respect to that basis. However for all xj, so β-0 and β2...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
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] .
solution of question d
(4 points) Consider the basis of R5 given by with b2 (2,-1,-5,-4,7), b3-(3, 2,-7,-5,9) b4 2,1,4,4,-5) bs (-1,0,1,2,0) The MATLAB code to produce the basis vectors is given by b1 11,0-2-2.3], b2 -12-1.-5-4,7T, b3 13-2-7-5,91, b4 [-2,14.4-5T, b5 1-1,0,1,20 Let S denote the standard basis for R a Find the transition matrix P P,s PB,s b. Use the previous answer to calculate the coordinate matrix of the vector z ( 1,5, 4, 3, 3) with respect...
2. Let T be the linear operator on C2 defined by Tc? = (1 + ?, 2), Te,-(i, i). Using the standard inner product, find the matrix of T* in the standard ordered basis. Does T commute with T*?
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
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...
JO # 2. Let the linear operator K : C([0, 1]) + C([0, 1]) be defined for each continuous real valued function f on [0, 1] by (Kf)(x) = 1 | tf(t) dt. a. Find a range of values for the parameter 1 for which the operator norm of K is strictly less than 1 with respect to the norm on C([0, 1]) given by Il gl. = sup{lg(t)| :te [0, 1]}. b. Describe an iterative process for solving (generating...
6. Let :P - P be the linear operator defined as (p(x)) - (5x), and let B = (1.x.x) be the standard basis for P2 a.) (5 points) Find the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x Determine (px)then find (p(x)) using (Tle from parta c.) (1 point) Check your answer to part b by evaluating T(x+6x) directly
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