(1 point) The matrix A = 1-6 1 8 k] 4 has two distinct real eigenvalues if and only if k > 24.5
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if (1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 [xii) Ic: aix has two distinct real eigenvalues if and only if k >
(1 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11 0 0 A= The eigenvalues are λ| < λ2 < λ3 < λ4, where has an eigenvector 12 has an eigenvector has an eigenvector 4 has an eigenvector Note: you may want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues
forget last questions, just count this one 11.5 Suppose that 4-LK 0<a<1,0<B<1, a +8 -1. a. Show that .= a, x= B. b. Show that MP, > 0, MPX>0; aq/al? <0,2q/ak? <0. c. Show that the RTS depends only on K/L, but not on the scale of production, and that the RTS (L. for K) diminishes as L/K increases. 11.5 Suppose that 4-LK 0<a<1,0<B<1, a +8 -1. a. Show that .= a, x= B. b. Show that MP, > 0,...
(1 point) Find the three distinct real eigenvalues of the upper-triangular matrix B= 5-7 0 0 7 -1 0 -97 -4 . 4 The eigenvalues are [Note: If there is more than one answer, separate them by commas. E.g. 1,2]
Complete this table relating the values of AGⓇ and K. AG <0 >1 = 1 <1
Problem 16 (10 pts) For an n x n matrix A, PA(t) = t.q(t) for some polynomial q(t) precisely when Det(A) = 0. Problem 17 (10 pts) If W CR” is a subspace and ve R", then pw(v) is the least-squares approximation to v by a vector in W except when pw(v) = 0. Problem 18 (10 pts) If A is a real n x n matrix, then the pairing defined by <v, w >:=yT * AT * A *W...
QUESTION 7 . 1 POINT Solve for 0 if 8sin 0 + 3 = 473 + 3 and 0 < 0 < 21. Select the correct answer below: O 0 = 4 and 0 = O 0 = only 0 = only 0 = 54 and = sa 0 = s only
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).