Question

solve system of linear using matrix method A-B+C=4
2A+B-3C=0
A+B+C=2 ​

Answer 1

Perform the Gauss Jordan elimination on the augmented matrix

A

=

⎛

⎜

⎝

1

3

2

∣

3

2

−

1

−

3

∣

−

8

5

2

1

∣

9

⎞

⎟

⎠

I have written the equations not in the sequence as in the question in order to get

1

as pivot.

Perform the folowing operations on the rows of the matrix

R

2

←

R

2

−

2

R

1

;

R

3

←

R

3

−

5

R

1

A

=

⎛

⎜

⎝

1

3

2

∣

3

0

−

7

−

7

∣

−

14

0

−

13

−

9

∣

−

6

⎞

⎟

⎠

R

2

←

R

2

−

7

A

=

⎛

⎜

⎝

1

3

2

∣

3

0

1

1

∣

2

0

−

13

−

9

∣

−

6

⎞

⎟

⎠

R

3

←

R

3

+

13

R

2

A

=

⎛

⎜

⎝

1

3

2

∣

3

0

1

1

∣

2

0

0

4

∣

20

⎞

⎟

⎠

R

3

←

R

3

4

A

=

⎛

⎜

⎝

1

3

2

∣

3

0

1

1

∣

2

0

0

1

∣

5

⎞

⎟

⎠

R

1

←

R

1

−

2

R

3

;

R

2

←

R

2

−

R

3

A

=

⎛

⎜

⎝

1

3

0

∣

−

7

0

1

0

∣

−

3

0

0

1

∣

5

⎞

⎟

⎠

R

1

←

R

1

−

3

R

2

A

=

⎛

⎜

⎝

1

0

0

∣

2

0

1

0

∣

−

3

0

0

1

∣

5

⎞

⎟

⎠

Thus

a

=

2

,

b

=

−

3

and

c

=

5

hope it helps you ✌️✅✅✅