Question 974316
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)