no calculator please 4. (12 pts) Show the matrix operator T: RR given by the following...
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
4. (12 pts) Show the matrix operator T: R3 R3 given by the following equations is one-to-one; Find the standard matrix for the inverse operator T-1, and find T-(W1, W2, W3). w1 = x1 +22-23 W2 = 2x1 +2:22 - 23 W3 = 21 - 2202
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, ).
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...
please explain all rhanks Search 19:24 If the probability that head is 1/2 and the probability that the back is 1/2, coin is repeatedly throws twice w1 (H,H) w2=(T,H) w3 (H,T) w4= (T,T) The sample space is {w1,w2,w3,w4} The random variable X: R and the random variable Y: R for all we, the probability P is and is defined P ((w)) X (w) 0 for we{w1,w3} X(w)=1, for w e (w2, w4} Y (w) 0, for we{w1,w2} Y(w)1, for w{w3,...
no calculator please 2. (12 pts) Given the matrix in a R R-E form: [1 0 0 0 3 -2 1 1 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity(AT). (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a basis for the null space of A.
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.
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...
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and corresponding eigenvectors vand v- 1? a. is a 2x2 matrix with repeated eigenvalue λ = 0 with defect 1 (has only one linearly independent eigenvector, not two.) and corresponding eigenvector vi- 13 (5 pts) Which of the direction fields corresponds to the system x -Cx, where...
4. Given the following signals, a) (6 pts). Find the signal energy in the voltage x(t) = 10rect b) (6 pts). Find the average signal power in the following periodic voltage, x(t). Express your answer in dBV 4AAK x(t) 9 10 11 12 Given the following amplifier 22 kn 56 kn o ww x(t) c) (6 pts). What is the loss in decibels? d) (7 pts). If the input to the amplifier is 3cos(2T300t+25°) V, what is the output in...