Question

D | Question 3 4 pts Solve the following system of equations using Gauss-Jordan elimination: 82-5y-5z =-11 The solution of this system of equations has the form z :-az + b, y # cz + d where z can be any real number in the spaces below, put the value of a in the first blank, the value of b in the second blank, the value of c in the third blank, and the value of d in the fourth blank.

Answer 1

First lets input the data into matrix form

First lets input the data into matrix form rightarrow (1 2 3 3 - 1 - 5 - 11 - 8 - 5 15 2 - 11) the matrix is same as Find the pivot in the 1st column in the 1st row Eliminate the 1st column R3 rightarrow R3-3R1 Make the pivot in the 2nd column by dividing the 2nd row by -7 R2 > R2(- 7) Eliminate the 2nd column R3 rightarrow R3 + 14R2 R1-- > R1 - 3R2 Therefore x_1 = 3 + 5x_3 = rightarrow x = az + b x_2 = 4 + 2x_3 = rightarrow y = cz + d a = 5 b = 3 c = 2 d = 4

the matrix is same as

	x1	x2	x3	b
1	1	3	-11	15
2	2	-1	-8	2
3	3	-5	-5	-11

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

Eliminate the 1st column R3 --> R3-3R1

	x1	x2	x3	b
1	1	3	-11	15
2	0	-7	14	-28
3	0	-14	28	-56

Make the pivot in the 2nd column by dividing the 2nd row by -7   

R2 --> R2/(-7)

	x1	x2	x3	b
1	1	3	-11	15
2	0	1	-2	4
3	0	-14	28	-56

Eliminate the 2nd column

R3 --> R3 + 14R2

	x1	x2	x3	b
1	1	3	-11	15
2	0	1	-2	4
3	0	0	0	0

R1-->R1 - 3R2

	x1	x2	x3	b
1	1	0	-5	3
2	0	1	-2	4
3	0	0	0	0

Therefore x₁ = 3+ 5x₃ ==> x = az + b

x₂ = 4 +2x₃ ==> y = cz + d

a = 5

b = 3

c = 2

d = 4

If you have any doubts please reply in here i will answer.Please rate the answer.Thank you