3. If T and S are similar in L(V) and also invertible does that imply that...
Let V and W be a vector spaces over F and T ∈ L(V, W) be invertible. Prove that T-1 is also linear map from W to V . Please show all steps, thank you
3. Suppose that T:V + V and S :V + V such that S is invertible. Prove that T and S-ITS have the same eigenvalues.
Let V be a vector space, let S, T L(V), and assume that ST = TS. Prove that if ˇ V is an eigenvector for T with eigenvalue λ, then λ is also an eigenvalue for S Find an eigenvector for λ with respect to S, and prove your answer is correct.
Let V be a vector space, let S, T L(V), and assume that ST = TS. Prove that if ˇ V is an eigenvector for T with eigenvalue...
Two n x n matrices A and B are called similar if there is an invertible matrix P such that B = P-AP. Show that two similar matrices enjoy the following properties. (a) They have the same determinant. (b) They have the same eigenvalues: specifically, show that if v is an eigenvector of A with eigenvalue 1, then P-lv is an eigenvector of B with eigenvalue l. (c) For any polynomial p(x), P(A) = 0 is equivalent to p(B) =...
Please give an example of a vector space V and linear transformations S,T from V to V such that ST may is invertible but one of S or T is not.
3. Let TEL(V,W), and assume that S E L(W) is an isometry. Prove that T and ST have the same singular values.
Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r], the set of all degree 2 or less polynomial functions. (c) Show that if A is invertible, then det A (Note: Show it for any det A-1 square matrix, showing it for a 2 x 2 matrix...
4) Why does ideal gas behavior imply that any gas's density in g/L is rel benavior imply that any gas's density in g/L is related to its molar mass? use complete sentences in your answer. A mathematical derivation is not necessary. 5) It was found that argon effused through a membrane in 24 hours, and an unknown gas diffused through the same membrane in 41.8 hours. What was the molecular weight of the gas?
I need the answer to problem 6
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 T : R3 →...
9. Current l(t) = 2e-21t - "Ult-3) A for t >0 and voltage V(t) is given as 28(t -3), then the circuit components are (a) R and C (b) Rand L (c) L and C (d) R only . La