The following systems of equations have unique solutions. Solve these systems us

Question

The following systems of equations have unique solutions. Solve these systems using the methods of Gauss Jordan elimination with matrices. (If your answer is dependent, use the parameter r as necessary. If there is no solution, enter No SOLUTION). a) 2x_1 + 4x_2 = 2 2x_1 + 7x_ 2 = 2 (x_1, x_2) = b) x_1 - 2x_2 - 6x_3 = -9 2x_1 - 6x_2 - 16x_3 = -26 x_1 + 2x_2 - x_3 = -2 (x_1, x_2, x_3) = c) x_2 + 2x_3 + 6x_4 = 46 x_1 - x_2 + x_3 + 5x_4 = 26 x_1 - x_2 - x_1 - 4x_4 = -20 3x_1 - 2x_2 - 6x_4 = -8 (x_1, x_2, x_3, x_4) =

Explanation / Answer

(A)Your matrix

Make the pivot in the 1st column by dividing the 1st row by 2

Eliminate the 1st column

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

Eliminate the 2nd column

Solution set:

x1 = 3

x2 = -1

(B)   

Your matrix

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

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by -2

Eliminate the 2nd column

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

Eliminate the 3rd column

Solution set:

x1 = 5

x2 = -2

x3 = 3

(C)

Your matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

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 -2

Eliminate the 3rd column

Make the pivot in the 4th column by dividing the 4th row by -9/2

Eliminate the 4th column

x1 = 112/9

x2 = 34/3

x3 = 6

x4 = 34/9

X1 X2 b 1 2 4 2 2 3 7 2

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