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Question 974316: Solve the following system of linear equations using matrices :
2X + 3Y + 3Z = 5
X – 2Y + Z = - 4
3X – Y – 2 Z = 3
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 2X + 3Y + 3Z = 5
X – 2Y + Z = - 4
3X – Y – 2 Z = 3
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That is a matrix.
There are several methods of solving it, but not "using matrices."
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2X + 3Y + 3Z = 5
X – 2Y + Z = -4
3X – Y – 2Z = 3
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I'll use elimination.
2X + 3Y + 3Z = 5 Eqn 1
2X – 4Y + 2Z = -8 Eqn 2 times 2
--------------------------- Subtract
7y + z = 13 Eqn A
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3X – 6Y + 3Z = -12 Eqn 2 times 3
3X – Y – 2Z = 3
------------------------------- Subtract
-5y + 5z = -15
Divide by -5
y - z = 3 Eqn B
7y + z = 13 Eqn A
------------------------------ Add
8y = 16
y = 2 ********************
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y - z = 3 Eqn B
z = -1 *******************
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X – 2Y + Z = - 4
x - 2*2 - 1 = -4
x = 1 ********************
(1,2,-1)
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