Math, asked by kunalkhade58, 2 months ago

13 std. solve the equation by matrix method 2x+3y=9,-x+y=-2​

Answers

Answered by kartikjalandhari113
0

Answer:

x=1,y=2 and z=−1

Step-by-step explanation:

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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