Only final answer no need for explaination

Section 1.5 Elementary Matrices: Problem 12 (1 point) Consider the following Gauss-Jordan reduction: -6 54 -9 1 0 0 1 EA EEA EEEA EEEE,A Find 1 0 0 E= 0 0 0 0 0 0 0 0 E, = 0 0 0 0 0 0 0 0 E3 = 0 0 0 0 0 0 0 0 0 EA = 0 0 0 0 0 0 Write A as a product A = E, 1E,E, 'E, 1 of elementary matrices: 000 00OI 1000 000 -6 0 54 -9 -9 = 1000 1000 10OO 0 0 1000Determine the following equivalent representations of the following system of equations: 5x + 4y = 2 -5x + 10y = -30 a. Find the augmented matrix of the system. 5 4 2 -5 10 -30 the matrix form of the system. 5 2 -5 10 -30 c. Use the inverse to satisfy the following matrix equation. -2 = 30 d. Find matrices that satisfy the following vector equation (i.e. find the vector form of the system). 5 4 10 e. The graph below shows the lines determined by the two equations in our system: 10 10 Find the coordinates of P =( 3 -3 Find the coordinates of y-intercept of the red line. A =(0, Find the coordinates of x-intercept of the green line. B =( 6 0)Consider the following two systems. (a) 6x + 2y = 2x - 3y = -1 (b) -6x + 2y = -3 2x - 3y = -4 (i) Find the inverse of the (common) coefficient matrix of the two systems. A-1 [88 ] (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A B where B represents the right hand side (i.e. B = for system (a) and B = for system (b)). Solution to system (@) = = Solution to system (b) = =Section 1.5 Elementary Matrices: Problem 5 {1 point] 11 Find the LU factorization of A = [ 5 1 [2: 3E] =[1Z] and use it to solve the system Section 1.5 Elementary Matrices: Problem 6 (1 point) -3 Find the LU factorization of A = 16 -13 1 -3 A = To solve the system 4 -1 -3 29 16 -1 -13 x = 117 8 1 -3 43 using the LU factorization, you would first solve Ly = and then solve Ux = Find the solution x =Section 1.5 Elementary Matrices: Problem 7 (1 point) -1 3 -2 Find the LU factorization of A = 3 5 3 -18 and use it to solve the system -3 2 3 5 3 3 -18 1 31 A = C1Section 1.5 Elementary Matrices: Problem 8 (1 point) Solve for X. Assume X is a 2 x 2 matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated. X =Section 1.5 Elementary Matrices: Problem 9 (1 point) Solve for X. Assume X is a 2 x 2 matrix and I denotes the 2 x 2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated. X =