x+y+z =9 ,x - 2y+3z= 8, 2x+y-z=3 solve by gauss Jordan method
Answers
Explanation:
sorry don't know the answer please don't mind
Answer:
The solution to the given system of equations is x = 20/7, y = -8/7, and z = 18/7.
Explanation:
To solve the given system of equations by the Gauss-Jordan method, we need to write the augmented matrix first:
[1 1 1|9]
[1 -2 3|8]
[2 1 -1|3]
To perform row operations, we'll use the following notation:
R1 = Row 1, R2 = Row 2, R3 = Row 3
We want to make the R1 coefficient in R2 to be zero. To do this, we'll subtract R1 from R2.
R1 = R1
R2 = R2 - R1
R3 = R3
[1 1 1|9]
[0 -3 2|-1]
[2 1 -1|3]
Next, we want to make the R1 coefficient in R3 to be zero. To do this, we'll subtract 2R1 from R3.
R1 = R1
R2 = R2
R3 = R3 - 2R1
[1 1 1|9]
[0 -3 2|-1]
[0 -1 -3|-15]
We want to make the R2 coefficient in R3 to be zero. To do this, we'll subtract 3R2 from R3.
R1 = R1
R2 = R2
R3 = R3 + 3R2
[1 1 1|9]
[0 -3 2|-1]
[0 0 -7|-18]
To get the reduced row echelon form, we'll divide R3 by -7, then add 2R3 to R2, and subtract R3 from R1.
R1 = R1 + R3
R2 = R2 + 2R3
R3 = (-1/7)R3
[1 1 0|27/7]
[0 -3 0|24/7]
[0 0 1|18/7]
To get the final solution, we'll back-substitute the values.
z = 18/7
-3y = 24/7
y = -8/7
x + 1 + 0 = 27/7
x = 20/7
To know more about the concept please go through the links:
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