NCERT Solutions class 12 Maths Exercise 4.6

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NCERT Solutions class 12 Maths Exercise 4.6 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

Download NCERT solutions for Determinants  as PDF.

NCERT Solutions class 12 Maths Exercise 4.6

NCERT Solutions class 12 Maths Determinants

Examine the consistency of the system of equations in Exercises 1 to 3.

1.  

Ans. Matrix form of given equations is AX = B

 

  A =  and B =

  =

Therefore, Unique solution and hence equations are consistent.


2.  

Ans. Matrix form of given equations is AX = B

  

  A =  and B =

  =

Therefore, Unique solution and hence equations are consistent.


3.

Ans. Matrix form of given equations is AX = B

  

 A =  and B =

  = 6 – 6 = 0

Now (adj. A) B =  =

Therefore, given equations are inconsistent, i.e., have no common solution.


Examine the consistency of the system of equations in Exercises 4 to 6.

4.  

Ans. Matrix form of given equations is AX = B

 

Here A =

 

  =   0

Therefore, Unique solution and hence equations are consistent.


5.  

Ans. Matrix form of given equations is AX = B

  

Here A =

 

  =  =

Now (adj. A) =

And (adj. A) B =  =  =

Therefore, given equations are inconsistent.


6.  

Ans. Matrix form of given equations is AX = B

  

Here A =

 

  =

Therefore, Unique solution and hence equations are consistent.


Solve the system of linear equations, using matrix method, in Exercise 7 to 10.

7.  

Ans. Matrix form of given equations is AX = B

  

Here    A = , X =  and B =

   =

Therefore, solution is unique and  =

 

=

Therefore,  and


8.  

Ans. Matrix form of given equations is AX = B

 

Here    A = , X =  and B =

  =

Therefore, solution is unique and  =

 

=

=

Therefore,  and


9.  

Ans. Matrix form of given equations is AX = B

 

Here    A = , X =  and B =

  =

Therefore, solution is unique and  =

 

=

=

Therefore,  and


10.  

Ans. Matrix form of given equations is AX = B

 

Here    A = , X =  and B =

  =

Therefore, solution is unique and  =

  =

Therefore,  and


NCERT Solutions class 12 Maths Exercise 4.6

Solve the system of linear equations, using matrix method, in Exercise 11 to 14.

11.  

Ans. Matrix form of given equations is AX = B

 

Here A =  , X =  and B =

  =  =

Therefore, solution is unique and  =

 

=

=

Therefore,  and


12.  

Ans. Matrix form of given equations is AX = B

 

Here    A =  , X =   and B =

 

=

=

Therefore, solution is unique and  =

 

=

=

Therefore,  and


NCERT Solutions class 12 Maths Exercise 4.6

13.  

Ans. Matrix form of given equations is AX = B

 

Here A =  , X =   and B =

 

=

=

Therefore, solution is unique and  =

 

=

=

Therefore,  and


14.  

Ans. Matrix form of given equations is AX = B

 

Here A =  , X =   and B =

 

=

=

Therefore, solution is unique and  =

 

=

=

Therefore,  and


NCERT Solutions class 12 Maths Exercise 4.6

15. If A =  find  Using  solve the system of equations    

Ans. Given: Matrix A =

 

  =

  exists and  ……….(i)

Now,  and  and

 adj. A =  =

 From eq. (i),

=

Now, Matrix form of given equations is AX = B

 

Here A =  , X =   and B =

Therefore, solution is unique and

 

=

=

Therefore,  and


NCERT Solutions class 12 Maths Exercise 4.6

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

Ans. Let ` ` ` per kg be the prices of onion, wheat and rice respectively.

 According to given data, we have three equations,

Matrix form of given equations is AX = B

 

Here A =  , X =   and B =

  =  =

Therefore, solution is unique and  =  …….(i)

Now,  

 adj. A =

 From eq. (i),

=

=

Therefore,  and

Hence, the cost of onion, wheat and rice are ` 5, ` 8 and ` 8 per kg.

NCERT Solutions class 12 Maths Exercise 4.6

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