# NCERT Solutions class 12 Maths Exercise 4.6

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## 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 =

=  =

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

### 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

### 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

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

Ans. Given: Matrix A =

=

exists and  ……….(i)

Now,  and  and

From eq. (i),

=

Now, Matrix form of given equations is AX = B

Here A =  , X =   and B =

Therefore, solution is unique and

=

=

Therefore,  and

### 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,

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

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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