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Write the system as a vector equation or matrix equation 14) Find the general solution of the homogeneous as indicated. system below. Give your answer as a vector. 12) Write the following system as a vector equation x1 + 2x2 - 3x3 = 0 involving a linear combination of vectors. 4x1 + 7x2 - 9x3 = 0 5x1 - 2x2 - X3 = 2 -x1 - 4x2 + 9x3 = 0 4x1 + 3x3 = -1 A ) X1 X1 X1 X1 A ) 5 x2 2-2 X2 x2 * 2 - w is EX X3 X3 x3 B (5] C) x1 2 + x 2 0 = - 1 X2 = X3 D) x1 5 +x2( 3 ]+x3[ 3' ]-[- 3 ] C *2 = X3 Solve the problem. D) [X1 x2 = X3 -3 Determine if the equation Ax = b is consistent for all possible b1, b2, b3. If the equation is not 15) Describe all solutions of Ax = b, where consistent for all possible b1, b2, b3, give a 2-5 37 A= -2 6 -5 and b= -5 description of the set of all b for which the equation is consistent (i.e., a condition which -47 0 must be satisfied by b1, b2, b3 ). A) Equation is consistent for all b1, b2, b3 Describe the general solution in parametric vector satisfying 9b1 + 6b2 + b3 = 0. form. B) Equation is consistent for all possible b1, b2, A) b3. x1 [-10 ] * 2 = -3 + x3 ONN C) Equation is consistent for all b1, b2, b3 EX satisfying -3b1 + b3 = 0. B) D) Equation is consistent for all b1, b2, b3 satisfying -b1 + b2 + b3 = 0. C = -10 ] [712 Ex + 8- D)