7. 0/10 points | Previous Answers WaneFMAC7 4.2.032. My Notes Use Gauss-Jordan r

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7. 0/10 points | Previous Answers WaneFMAC7 4.2.032. My Notes Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of X, where y = y(x) and z = z(x).) 0.75x-0.5y + 0.25z = 15 y+ x+ (x, y, z) = Submit Answer Save Progress Practice Another Version 8. 0/10 points | Previous Answers WaneFMAC7 4.2.033 My Notes Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x), z = z(x), and w = w(x).) x+3y + 11z + 2w = 1 x+ y+ 3z + w=-3 (x, y, z, w) =

Explanation / Answer

Augmented matrix for given system of equations

Using Gauss-Jordan elimination

Your matrix

X1   X2   X3   b
1   1   1   -1   -4
2   1   -1   -7   2
3   0.75   -0.5   0.25   15
4   1   1   1   2
Find the pivot in the 1st column in the 1st row

X1   X2   X3   b
1   1   1   -1   -4
2   1   -1   -7   2
3   0.75   -0.5   0.25   15
4   1   1   1   2
Eliminate the 1st column

X1   X2   X3   b
1   1   1   -1   -4
2   0   -2   -6   6
3   0   -1.25   1   18
4   0   0   2   6
Make the pivot in the 2nd column by dividing the 2nd row by -2

X1   X2   X3   b
1   1   1   -1   -4
2   0   1   3   -3
3   0   -1.25   1   18
4   0   0   2   6
Eliminate the 2nd column

X1   X2   X3   b
1   1   0   -4   -1
2   0   1   3   -3
3   0   0   4.75   14.25
4   0   0   2   6
Make the pivot in the 3rd column by dividing the 3rd row by 4.75

X1   X2   X3   b
1   1   0   -4   -1
2   0   1   3   -3
3   0   0   1   3
4   0   0   2   6
Eliminate the 3rd column

X1   X2   X3   b
1   1   0   0   11
2   0   1   0   -12
3   0   0   1   3
4   0   0   0   0
Solution set:

x = 11
y = -12
z = 3

(x, y, z) = ( 11, -12, 3). Answer

(B)

Augmented matrix for given system of equations

Using Gauss-Jordan elimination

Your matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by -8

Eliminate the 3rd column

Find the pivot in the 4th column in the 4th row

Eliminate the 4th column

Solution set:

x= -9/2

y= 0

z = 1/2

w = 0

X1 X2 X3 X4 b 1 1 1 3 0 -3 2 0 1 8 1 4 3 1 3 11 2 1 4 1 1 3 1 -3

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