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Question 1141227: Greeting sir,I would like to ask a question about matrices.the question is below as shown and I need to find it by using the elimination method or the augmented matrix.I have tried to do it but it seems like I stuck because at Row 3 Column 3,(A33) I got zero as it was suppose to be 1 since it need to be identity.Can you help me to find the unknown x,y,z?
Solve the following systems of linear equations by using elimination method. State whether it is inconsistent or has infinitely many solutions.
5𝑥 −4𝑦 +𝑧 = 0
𝑥 +𝑦 = 0
−10𝑥 +8𝑦 −2𝑧 = 0
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A33 will only be 1 if the system of equations is consistent and has a unique solution. In this system, the 0 in A33 tells you that the system has infinitely many solutions.
5 -4 1 0
1 1 0 0
-10 8 -2 0
Switch rows 1 and 2 to make A11=1; replace row 3 with row 3 plus -2 times row 1:
1 1 0 0
5 -4 1 0
0 0 0 0
Replace row 2 with row 2 minus 5 times row 1, to make A21=0:
1 1 0 0
0 -9 1 0
0 0 0 0
The reduced system of equations is
x+y = 0
-9y+z = 0
Since both equations involve y, use y=t to define the set of solutions parametrically.
x = -y
z = 9y
y = t
x = -t
z = 9t
The system of equations has infinitely many solutions; the solution set is any triple (x,y,z) of the form (-t,t,9t).
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