Consider the linear system X'=AX,where 4= and A is a 2 x 2 matrix. Which of the following statements is True? 10 -6t O a If X1 = -10 19- are two linearly dependent solutions, then the general solution is X=C1X1+C2X1 and X2= -30 le 30 1 Ob.If X1 = -3 -6t and X2- eSt are two linearly independent solutions, then the general solution is X=c1X+c2X2. Oc If X1= -1 -3 -6t and X2= St are two linearly independent solutions, then the general solution is X=cjX+€2X1 1 10 e-6t and X2= -30 le-6t are two linearly dependent solutions, then the general solution is X=c1X1+c2X2 Od. = Lx JI -10 30 No correct answer

Write the system of linear equations in the form Ax = b. Then use Gaussian elimination to solve this matrix equation for x. X2 + x3 = -6 - 3x1 - 2x1 + 4x2 5x3 = 5 X1 2x2 + 3x3 = 0 X1 8- X2 = X3 X1 349 X2 5 X3 0 сл

Write the system of linear equations -3x + ly – 9z 8 6x + 4y – 4z 5 7x + 3y – 9z as a matrix equation. ||||

I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3