66. Suppose a non-homogeneous system AF = 5 of six linear equations in eight variables has...
6 7. Let A be a 4 x 4 matrix. The eigenvectors of A are 6 and –5. The eigenspace corresponding to 1 = 6 is 2-dimensional and the eigenspace corresponding to 1 = -5 is 1-dimensional. Is A diagonalizable? Why or why not?
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
02. (8,2, 5) You are provided with a system of linear equations Ax - ye, where A R r ER2,yER2 and e e Ri. Let the spectral decomposition of A is given by V2/2 V2/2( containing 1 0 containing eigenvalues of A and V2/22/2 Lo 5 corresponding orthonormal eigenvectors a) Determine the best approximation of the unknow vector x, when the observerd vector y 181 02. (8,2, 5) You are provided with a system of linear equations Ax - ye,...
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
need answer for qustion2&3. 5:17 childsmath.ca on the answer sheet below. Problem #1: On a certain island, there is a population of snakes foxes, hawks and mice. Their populations at time t are given by st), f(), h), and m(t) respectively The populations grow at rates given by the differential equations 0h + h'= m - 4+- m' u유-49 +/준-s유 Putting the y) [s)f() h() m(t)]7, this system can be written as y' Ay four populations into vector Find the...