Math, asked by tabibupokemon666, 4 hours ago

TP 3 : Solve the simultaneous
equations. 5x - 2y - 4z = 3, 3x + 3y +
2z = -3, -2x + 5y + 3z = 3*

Answers

Answered by sakshisingh987
0

Answer:

Given system of linear equations are

2x+3y+3z=5

x−2y+z=−4

3x−y−2z=3.

Represent it in matrix form

2

1

3

3

−2

−1

3

1

−2

x

y

z

=

5

−4

3

which is in the form of AX=B

A=

2

1

3

3

−2

−1

3

1

−2

∣A∣=10+15+15=40

=0

∴ A

−1

exists

To find adjoint of A

A

11

=5,A

12

=5,A

13

=5

A

21

=3,A

22

=−13,A

23

=11

A

31

=9,A

32

=1,A

33

=−7

Adj(A)=co-factor

5

3

9

5

−13

1

5

11

−7

=

5

5

5

3

−13

11

9

1

−7

A

−1

=

∣A∣

1

Adj(A)

=

40

1

5

5

5

3

−13

11

9

1

−7

X=A

−1

B

=

40

1

5

5

5

3

−13

11

9

1

−7

5

−4

3

X=

40

1

25−12+27

25+52+3

25−44−21

X=

40

1

40

80

−40

x

y

z

=

1

2

−1

Hence, x=1,y=2 and z=−1

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