Please answer the following questions with clear working out.
09.
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Please answer the following questions with clear working out.
09.
3. (a) Let M- (i) Find...
please answer in details , with clear handwritten, 3. Let T: V- V be a linear...
please answer in details , with clear handwritten,
3. Let T: V- V be a linear transformation on a 3-dimensional vector space V, with basis B- (v,2, v3 ff TW C w. A subspace W CV is invariant under T' 1 (a) Prove that if W and W2 are invariant subspaces under T, then Winw2 and Wi+W2 are invariant under T. (b) Find conditions a matrix representation Ms (T) such that the following subspaces are invariant under T span vspan...
Q10 10 Points Please answer the below questions. Q10.1 4 Points Let m, n EN\{1}, V...
Q10 10 Points Please answer the below questions. Q10.1 4 Points Let m, n EN\{1}, V be a vector space over R of dimension n and (v1,..., Vm) be an m tuple of V. (Select ALL that are TRUE) If m > n then (v1, ..., Vy) spans V. If (01,..., Vm) is linearly independent then m <n. (V1,..., Um) is linearly dependent if and only if for all i = 1,..., m we have that Vi Espan(v1,..., Vi-1, Vi+1,...,...
3. (16pts) (a) (4pts) Show that if I co(A), then 13 € O(A). (b) (4pts) Let...
3. (16pts) (a) (4pts) Show that if I co(A), then 13 € O(A). (b) (4pts) Let T1, T2: V + V be two linear operators, such that ToT2 = Ti and T20T = T2. Show that Ker(T) Ker(T) and Ker(T) Ker(T) (c) (4pts) Let T :V + W be a linear transformation. If T is One-to-One and vi, 02, ..., Uk are linearly independent vectors in V, show that T(01), T(02),... ,T(Uk) are also linearly independent. (11) (d) (4pts) Find...
Please answer me fully with the details. Thanks! True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linear...
Please answer me fully with the details. Thanks!
True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linearly independent subset of (1) Let V bea vector spacе, аnd let dim(V) V. then n < т. (2) Let V and W be vector spaces, and suppose that T : V -+ W is a linear transformation. If there are vectors i, 2, ..., Tj in V such that the vectors T(),T(T2),...,T(vj) span W, then the...
Please help, and provide some explanation if possible! Thank you :) (1) Answer the following questions (a) Let T : R3 → R2 be such that (i) Find a matrix A such that T(E) Az. (i) Find T(2,-3,5). (iii...
Please help, and provide some explanation if possible! Thank you
:)
(1) Answer the following questions (a) Let T : R3 → R2 be such that (i) Find a matrix A such that T(E) Az. (i) Find T(2,-3,5). (iii) Is the transformation T invertible? YES No (b) The smiley face shown at the top of the figure is transformed by various linear transformations represented by matrices A - F. Find out which matrix does which transformation. Write the letter of...
I need the answer to problem 4 (exercises 1, 2, 3) Clear and step by step...
I need the answer to problem 4 (exercises 1, 2,
3)
Clear and step by step please
Problem 4. Let V be a vector space and let T : V → V and U : V → V be two linear transforinations 1. Show that. TU is also a linear transformation. 2. Show that aT is a linear transformation for any scalar a. 3. Suppose that T is invertible. Show that T-1 is also a linear transformation. Problem 5. Let...
Please answer the following question. Thank you. 30. Let T:V W be a linear transformation from...
Please answer the following
question. Thank you.
30. Let T:V W be a linear transformation from a vector space V into a vector space W.Prove that the range of T is a subspace of W.[ Hint: Typical elements of the range have the form T(x) and T(w) for some x, w in V.]
(1) (Definition and short answer — no justification needed) (a) Let f:R → R", and let...
(1) (Definition and short answer — no justification needed) (a) Let f:R → R", and let p ER". Define carefully what it means for the function f to be differentiable at p. (b) Given a linear transformation T : R" + R", explain briefly how to form its representing matrix (T). If you know the matrix (T), how can you compute T(v) for a vector v € R"? 1 and let S be the linear (c) Let T be the...
please i need the question 15 for the detailed proof and explaination ! thanks ! 233 42 Isometries, Conformal Maps 14,...
please i need the question 15 for the detailed proof and
explaination ! thanks !
233 42 Isometries, Conformal Maps 14, we say that a differentiable map ф: S,--S2 preserves angles when for every p e Si and every pair vi, v2 E T (S,) we have cos(u, 2) cos(dp, (vi). do,()). Prove that pis locally conformal if and only if it preserves angles. 15. Letp: R2 R2 be given by ф(x, y)-(u (x, y), u(x, y), where u and...
(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector...
(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector 90 degrees counterclockwise. Let A be the standard matrix for T. Is A diagonalizable over R? What about over C? (e) (3 points) Let T : R4 → R4 be given by T(x) = Ax, A = 3 -1 7 12 0 0 0 4 0 0 5 4 0 4 2 1 Is E Im(T)? 3 (f) (9 points) Let U be a...
please answer in details , with clear handwritten,
3. Let T: V- V be a linear transformation on a 3-dimensional vector space V, with basis B- (v,2, v3 ff TW C w. A subspace W CV is invariant under T' 1 (a) Prove that if W and W2 are invariant subspaces under T, then Winw2 and Wi+W2 are invariant under T. (b) Find conditions a matrix representation Ms (T) such that the following subspaces are invariant under T span vspan...
Q10 10 Points Please answer the below questions. Q10.1 4 Points Let m, n EN\{1}, V be a vector space over R of dimension n and (v1,..., Vm) be an m tuple of V. (Select ALL that are TRUE) If m > n then (v1, ..., Vy) spans V. If (01,..., Vm) is linearly independent then m <n. (V1,..., Um) is linearly dependent if and only if for all i = 1,..., m we have that Vi Espan(v1,..., Vi-1, Vi+1,...,...
3. (16pts) (a) (4pts) Show that if I co(A), then 13 € O(A). (b) (4pts) Let T1, T2: V + V be two linear operators, such that ToT2 = Ti and T20T = T2. Show that Ker(T) Ker(T) and Ker(T) Ker(T) (c) (4pts) Let T :V + W be a linear transformation. If T is One-to-One and vi, 02, ..., Uk are linearly independent vectors in V, show that T(01), T(02),... ,T(Uk) are also linearly independent. (11) (d) (4pts) Find...
Please answer me fully with the details. Thanks!
True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linearly independent subset of (1) Let V bea vector spacе, аnd let dim(V) V. then n < т. (2) Let V and W be vector spaces, and suppose that T : V -+ W is a linear transformation. If there are vectors i, 2, ..., Tj in V such that the vectors T(),T(T2),...,T(vj) span W, then the...
Please help, and provide some explanation if possible! Thank you
:)
(1) Answer the following questions (a) Let T : R3 → R2 be such that (i) Find a matrix A such that T(E) Az. (i) Find T(2,-3,5). (iii) Is the transformation T invertible? YES No (b) The smiley face shown at the top of the figure is transformed by various linear transformations represented by matrices A - F. Find out which matrix does which transformation. Write the letter of...
I need the answer to problem 4 (exercises 1, 2,
3)
Clear and step by step please
Problem 4. Let V be a vector space and let T : V → V and U : V → V be two linear transforinations 1. Show that. TU is also a linear transformation. 2. Show that aT is a linear transformation for any scalar a. 3. Suppose that T is invertible. Show that T-1 is also a linear transformation. Problem 5. Let...
Please answer the following
question. Thank you.
30. Let T:V W be a linear transformation from a vector space V into a vector space W.Prove that the range of T is a subspace of W.[ Hint: Typical elements of the range have the form T(x) and T(w) for some x, w in V.]
(1) (Definition and short answer — no justification needed) (a) Let f:R → R", and let p ER". Define carefully what it means for the function f to be differentiable at p. (b) Given a linear transformation T : R" + R", explain briefly how to form its representing matrix (T). If you know the matrix (T), how can you compute T(v) for a vector v € R"? 1 and let S be the linear (c) Let T be the...
please i need the question 15 for the detailed proof and
explaination ! thanks !
233 42 Isometries, Conformal Maps 14, we say that a differentiable map ф: S,--S2 preserves angles when for every p e Si and every pair vi, v2 E T (S,) we have cos(u, 2) cos(dp, (vi). do,()). Prove that pis locally conformal if and only if it preserves angles. 15. Letp: R2 R2 be given by ф(x, y)-(u (x, y), u(x, y), where u and...
(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector 90 degrees counterclockwise. Let A be the standard matrix for T. Is A diagonalizable over R? What about over C? (e) (3 points) Let T : R4 → R4 be given by T(x) = Ax, A = 3 -1 7 12 0 0 0 4 0 0 5 4 0 4 2 1 Is E Im(T)? 3 (f) (9 points) Let U be a...
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