Determinants(Ex. 4.6)

Exercise 4.6

Solve system of linear equations, using matrix method, in Exercise 7 to 14.

7. 5x+2y = 4

    7x+3y = 5

Solun:- Given equations represent in matrix form:-

⇒ AX = B

We know that X = A-1B

Compare corresponding elements

⇒ x=2, y=-3

8. 2x-y = -2

    3x+4y = 3

Solun:- Given equations represent in matrix form:-

⇒ AX = B

We know that X = A-1B

Compare corresponding elements

⇒ x= - 5/11, y=12/11

9. 4x-3y = 3

    3x-5y = 7

Solun:- Given equations represent in matrix form:-AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x= - 6/11, y = - 19/11

10. 5x+2y = 3

      3x+2y = 5

Solun:- Given equations represent in matrix form:-AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x= - 1, y = 4

11. 2x+y+z = 1

      x-2y-z = 3/2

      3y-5z = 9

Solun:- Given equations represent in matrix form:-AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x= 1, y = 1/2,  z= - 3/2

12. x-y+z = 4

      2x+y-3z = 0

      x+y+z = 2

Solun:- Given equations represent in matrix form:-

 AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x = 2, y = -1,  z = 1

13. 2x+3y+3z = 5

      x-2y+z = -4

      3x-y-2z = 3

Solun:- Given equations represent in matrix form:- AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x = 1, y = 2,  z = - 1

14 . x-y+2z = 7

      3x+4y-5z = -5

      2x-y+3z = 12

Solun:- Given equations represent in matrix form:- AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x = 2, y = 1,  z = 3

2x-3y+5z = 11

3x+2y-4z = -5

x+y-2z = -3

Solun:- We know that A-1 = 1/|A| (adj A) 

Given Eq. 

2x-3y+5z = 11

3x+2y-4z = -5

x+y-2z = -3

Given equations represent in matrix form:- AX = B 

We know that X = A-1B

Compare corresponding elements

⇒ x = 1, y = 2,  z = 3

16. The cost of 4 kg onion, 3 kg wheat, and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat, and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

Solun:- Let the cost of 1 kg onion is = x

the cost of 1 kg wheat is = y

the cost of 1 kg rice is = z

⇒ 4x+3y+2z = 60

⇒ 2x+4y+6z = 90

⇒ 6x+2y+3z = 70

Apply Matrix method and represent in matrix form:- AX = B

We know that X = A-1B

So, the cost of 1 kg onion is = 5 Rs

the cost of 1 kg wheat is = 8 Rs

the cost of 1 kg rice is = 8 Rs

Download Pdf of Exercise 4.6

See Also:-

Notes of Determinants

Exercise 4.1

Exercise 4.3

Exercise 4.4

Exercise 4.5

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