Let A = [1 -2 3 -3 5 -6 2 -1 -3] and b = [b_1 b_2 b_3]. Determine if the equation Ax = b is consistent for all possible b_1, b_2, b_3. If the equation is consistent for all possible b_1, b_2, b_3, give a description of the set of all b for which the consistent (i.e., a condition which must be satisfied by b_1, b_2, b_3). A) Equation is consistent for all b_1, b_2, b_3 satisfying - b_1 + b_2 + b_3 = 0. B) Equation is consistent for all possible b_1, b_2, b_3. C) Equation is consistent for all b_1, b_2, b_3 satisfying 3b_1 + 3b_2 + b_3 = 0. D) Equation is consistent for all b_1, b_2, b_3 satisfying -3b_1 + b_3 = 0. Find the general solution of the homogeneous system below. Give your answer as a x_1 + 2x_2 - 3x_3 = 0 4x_1 + 7x_2 - 9x_3 = 0 -x_1 - 4x_2 + 9x_3 = 0 A) [x_1 x_2 x_3] = x_3 [3 -3 1] B) [x_1 x_2 x_3] = x_3 [-3 3 1] C) [x_1 x_2 x_3] = [-3 3 1] D) [x_1 x_2 x_3] = x_3 [-3 3 0]
Show transcribed image textLet A = [1 -2 3 -3 5 -6 2 -1 -3] and b = [b_1 b_2 b_3]. Determine if the equation Ax = b is consistent for all possible b_1, b_2, b_3. If the equation is consistent for all possible b_1, b_2, b_3, give a description of the set of all b for which the consistent (i.e., a condition which must be satisfied by b_1, b_2, b_3). A) Equation is consistent for all b_1, b_2, b_3 satisfying - b_1 + b_2 + b_3 = 0. B) Equation is consistent for all possible b_1, b_2, b_3. C) Equation is consistent for all b_1, b_2, b_3 satisfying 3b_1 + 3b_2 + b_3 = 0. D) Equation is consistent for all b_1, b_2, b_3 satisfying -3b_1 + b_3 = 0. Find the general solution of the homogeneous system below. Give your answer as a x_1 + 2x_2 - 3x_3 = 0 4x_1 + 7x_2 - 9x_3 = 0 -x_1 - 4x_2 + 9x_3 = 0 A) [x_1 x_2 x_3] = x_3 [3 -3 1] B) [x_1 x_2 x_3] = x_3 [-3 3 1] C) [x_1 x_2 x_3] = [-3 3 1] D) [x_1 x_2 x_3] = x_3 [-3 3 0]