aving the four states (0, 0), (0, 1), (1, natrix.

The LU factorization of A = = A = 1 1 1 -1 -2 Ly= To solve the system 2 -1 2 0 01 1 0 -3 Ux: = -4 and then solve 0-2 10 0 X = 2 2 -2 5 -18] -26 Find the solution x = ܝ -3 L-2 5 42 using the LU factorization, you would first solve 2 0 -2 22 2 2 is -4]

Find x1, x2, x3 with gauss jordan

Find the least-squares solution * of the system 1 01 0 1i 0 0 5 2. || ||

Roll a fair sided die three times. Let A1 = {1 or 2 on the first roll }, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai ) = 1/3, i = 1,2,3; P(Ai intersection Aj) = (1/3)2 , i cannot equal j; and P(A1 intersection A2 intersection A3) = (1/3)3 a) use theorem 1.1-6 to find P(A1 union A2 union A3) b) show that P(A1 union A2 union A3) = 1-(1-1/3)3

2.3 8. pls help

3 1 = ( ₁²3 ) E3.4. (20) Show that the matrix A= second power of A). -2 is invertible and find A¯² (the negative

A system of ordinary differential equations has an equilibrium point at the origin with the Jacobian matrix  J =  [0   1][-3  0]    what is the classification of the linearised system of equations at this equilibrium point? - Sink, centre, spiral source or star source?