Question

solve the following system of equations using matrices(row operations). If the system has no solution, say that it is inconsistent

This Question: 1 pt 4 of 10 (7 complete) Thie Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -x + y + Z=-3 -x + 4y - 8z = -21 6x - 3y - 15z = 0 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The solution is ( C. (Simplify your answers.) OB. There are infinitely many solutions. The solution can be written as {(x,y,z)/x = 1. z is any real number}. (Simplify your answers. Type expressions using z as the variable.) OC. There are infinitely many solutions. The solution can be written as {«.,2)/x- |||.y is any real number, z is any real number} (Simplify your answer. Type an expression using y and z as the variables.) OD. The system is inconsistent Click to select and enter your answer(s).

Answer 1

Solution -1 + y + z = -3 -x + 4y - 82 = 21 67 – 3y - 15z = Augmented materia I ·l 4 -8 -21 6 -3 -15 -3 R2-R, R2 17 1 3 -3 *3 -18 -9 -IS 6. Rg+6R, R3 1 -g -3 -18 -18 3 Rzr R2 → R3 1 -3 We "Oo oo our ocó our -91-18 R2 > R2 oft 1 -3 -6

-2 + y + z =-3 eq-(1) Y-32 -6 -eq-(2) let Z. Z from eqa (2) - y=-6+32 from eg. (1) - -X=-3-4-2 *= 3+ ytz x 3+(-6+32)+2 d=3-6+ 3ztz ez-zt uz -3+uz: X = -6+ 3 Z Z > 3 B There are infinitely many solutions. The solution can be written as {(X,Y,Z) 1 x = -3+42, y=-6+32, 2 is any real number} .