4. (12 pts) Show the matrix operator T: R3 R3 given by the following equations is...
no calculator please 4. (12 pts) Show the matrix operator T: RR given by the following equations is one-to-one; Find the standard matrix for the inverse operator T-I, and find T-(W1, W2, w3). w1 = x +22-23 w2 = 2.v 1 + 2x2 - 23 W3 = x - 2.12
4. (12 pts) Show the matrix operator T: RR given by the following equations is one-to-one; Find the standard matrix for the inverse operator T-l, and find T-(W1, 2, 3). w = x - 2:02 +2:23 w2 = 2.rı -23 W3 = 2.11 - 12 +23
Problem 4. Let B = {V1, 02, 03} CR, where [3] [1] 01 = 12, 02 = 12103 = 1 [1] [2] 4.1. Show that the matrix A = (v1 V2 V3) E M3(R) is invertible by finding its inverse. Conclude that B is a basis for R3. 4.2. Find the matrices associated to the coordinate linear transformation T:R3 R3, T(x) = (2]B- and its inverse T-1: R3 R3. Use your answers to find formulas for the vectors 211 for...
AB matrix, linear operator R2 into R3 find the standard fro 11) For the linear operator L(x1, 22, ^1 + 22 AB matrix, linear operator R2 into R3 find the standard fro 11) For the linear operator L(x1, 22, ^1 + 22
3. (12 pts) Find a subset of vectors that forms a basis for the space spated by 11 = (1.22. - 1), 1 = (-3, -6, -6,3). Es =(4,9,9,-4), 4 = (-2,-1,-1,2), 3 =(5,8,9,-5). Then express the other vector(s) as a linear combination of the basis vectors 4. 12 pts) Show the matrix operator T: - R given by the following equations is one-to-one Find the standard matrix for the inverse operator T-!, and find T-2, 43, ).
Please show work Consider the following linear transformation T: RS → R3 where T(X1, X2, X3, X4, Xs) = (x1-X3+X4, 2x1+x2-X3+2x4, -2x1+3x3-3x4+xs) (a) Determine the standard matrix representation A of T(x). (b) Find a basis for the kernel of T(x). (c) Find a basis for the range of T(x). (d) Is T(x) one-to-one? Is T(x) onto? Explain. (e) Is T(x) invertible? Explain
3. (10 points) Let T : R3-A, T(x1, 22, 23) = (zi,-z2,23 a) Prove that T is a linear operator. b) Find the standard matrix of T.
only do (e)-(g) The linear operator L : R3 + R3 is given by its matrix A = Al,s wit respect to the standard basis S = {(1, 22, 23}, where To 0 11 -10- 20 [4 00 (a) Find the characteristic polynomial PL(x) of L; (b) What are the eigenvalues of L and what are their algebraic multiplicities? (e) What are the geometric multiplicities of eigenvalues of L? Is L diagonal- izable? (d) Find a basis B of eigenvectors...
5. Given a linear map f R3R3 if V Vi, V2, va) is a basis of R3, and further, a) State the defining matrix of f under the basis vi, V2, vs) -3 2 0 b) Let W-(w1, w2, w3) be another basis of R3 and P42 be the change- 01-1 of-coordinate matrix from V to W. Let A be the defining matrix for f under the basis W diagonalize A. 5. Given a linear map f R3R3 if V...
12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/4 0 -1; 01/26; 1/204) (20 pts)Find the inverse of the matrix from question 12. I te To keep up-to-date with security updates, fixes, and improvements, choose Check for Upd c (2-1) 12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/40-1; 01/26;1/204) (20 pts) Find the inverse of the matrix from question 12.