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6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B...
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
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B...
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [T]s, the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x?. 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+6x²) directly.
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) =...
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) = p(5x), and let B = {1,x, x2} be the standard Find [T]b, the matrix for T relative to B. Let p(x) = x + 6x2. Determine [p(x)]B, then find T(p(x)) using [T]s from part a. Check your answer to part b by evaluating T(x + 6x2) directly.
6. Let T: P, – P, be the linear operator defined as T(p(x)) = p(5x), and...
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.
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*?
could u help me for this question?thanku!! 21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x...
could u help me for this question?thanku!!
21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T.
21. Let T...
10. Let T : P P , be the linear transformation defined by T(P) = (a)...
10. Let T : P P , be the linear transformation defined by T(P) = (a) What is the kernel of T? (b) According to the concept of the rank theorem, what is the dimension of the range of T? (C) (needs an idea from earlier in the semester) If we represent P, by coordinate vectors rela- tive to it's standard basis (1.1.1-.1') and P, by coordinate vectors relative to it's standard basis (1,1,1"), find the standard matrix A of...
Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that...
Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that is T(CO + C1x + c2x2) = co+C1(4x + 5) + c2(4x + 5)2. Find [7]3 with respect to the basis B = {1, x, x?}. Enter the second row of the matrix [7]z into the answer box below. i.e.. if A = [7]B. then enter the values a21, a22, 223, (in that order), separated with commas.
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...
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where...
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where A=12 0-2 and let 0 0 Find the transition matrix V corresponding to a change of basis from i,V2. vs) to e,e,es(standard basis for R3), and use it to determine the matrix B representing L with respect to (vi, V2. V
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
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [T]s, the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x?. 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+6x²) directly.
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) = p(5x), and let B = {1,x, x2} be the standard Find [T]b, the matrix for T relative to B. Let p(x) = x + 6x2. Determine [p(x)]B, then find T(p(x)) using [T]s from part a. Check your answer to part b by evaluating T(x + 6x2) directly.
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.
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*?
could u help me for this question?thanku!!
21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T.
21. Let T...
10. Let T : P P , be the linear transformation defined by T(P) = (a) What is the kernel of T? (b) According to the concept of the rank theorem, what is the dimension of the range of T? (C) (needs an idea from earlier in the semester) If we represent P, by coordinate vectors rela- tive to it's standard basis (1.1.1-.1') and P, by coordinate vectors relative to it's standard basis (1,1,1"), find the standard matrix A of...
Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that is T(CO + C1x + c2x2) = co+C1(4x + 5) + c2(4x + 5)2. Find [7]3 with respect to the basis B = {1, x, x?}. Enter the second row of the matrix [7]z into the answer box below. i.e.. if A = [7]B. then enter the values a21, a22, 223, (in that order), separated with commas.
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...
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where A=12 0-2 and let 0 0 Find the transition matrix V corresponding to a change of basis from i,V2. vs) to e,e,es(standard basis for R3), and use it to determine the matrix B representing L with respect to (vi, V2. V
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