Math Homework MTH110-400 Finite Math (N. Cross) SP18 Homework: Homework 6: Score
ID: 3170012 • Letter: M
Question
Math Homework MTH110-400 Finite Math (N. Cross) SP18 Homework: Homework 6: Score: 0 of 1 pt 6.2.41 Section 6.2 rk 14 of 14 (8 complete) & Tests Previous Question -15x-9y--4 pok Solve the folowing system of equations using the Gauss-Jordan method Select the cormect choice below and, id necessary, fill in the answer baxes to complete your choice on Thes system has exact yore solution. The solutonis(ALE) OB. This systerm has infintely many solutions of the frmC1z).where z is any real number O C. Ths system has no soution 12x + 9y+ z= -2 Contents dia Library se Options n Tutor Type an exact answer in simplitied form.) (Type expressions using z as the variable.) aTools Click to select and enter your answer(s) and then click Check Answer. Clear Al ASUSExplanation / Answer
The augmented matrix of the given system of linear equations is A (say) =
-15
-9
-1
-4
-9
-15
-2
25
12
9
1
-2
To solve the given system of linear equations, we will reduce A to its RREF as under:
Multiply the 1st row by -1/15
Add 9 times the 1st row to the 2nd row
Add -12 times the 1st row to the 3rd row
Multiply the 2nd row by -5/48
Add -9/5 times the 2nd row to the 3rd row
Multiply the 3rd row by -16
Add -7/48 times the 3rd row to the 2nd row
Add -1/15 times the 3rd row to the 1st row
Add -3/5 times the 2nd row to the 1st row
Then the RREF of A is
1
0
0
2
0
1
0
-3
0
0
1
1
Thus, the solution of the given system of linear equations is x = 2, y = -3 and z = 1 i.e. (x,y,z)T = (2,-3,1)T. Option A is the correct answer.
-15
-9
-1
-4
-9
-15
-2
25
12
9
1
-2