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# Solutions 4. Determinants - Exercise 4.6 | Class 12 Mathematics-I - Toppers Study

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## Solutions 4. Determinants - Exercise 4.6 | Class 12 Mathematics-I - Toppers Study

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### You can Find Mathematics-I solution Class 12 Chapter 4. Determinants

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Chapter 4 Mathematics-I class 12

### Exercise 4.6 class 12 Mathematics-I Chapter 4. Determinants

Sure! The following topics will be covered in this article

- Solutions 4. Determinants - Exercise 4.6 | Class 12 Mathematics-I - Toppers Study
- Class 12 Ncert Solutions
- Solution Chapter 4. Determinants Class 12
- Solutions Class 12
- Chapter 4. Determinants Exercise 4.6 Class 12

## 4. Determinants

### | Exercise 4.6 |

## Solutions 4. Determinants - Exercise 4.6 | Class 12 Mathematics-I - Toppers Study

**Exercise - 4.6**

**Examine the consistency of the system of equations in Exercises 1 to 6.**

**Ques.1. **** **

**Ans. **Matrix form of given equations is AX = B

A = and B =

=

There has Unique solution and hence equations are consistent.

**Ques.2. **** **

**Ans. **Matrix form of given equations is AX = B

A = and B =

=

There has Unique solution and hence equations are consistent.

**Ques.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.

**Ques.4. **** **

**Ans. **Matrix form of given equations is AX = B

A =

= 0

There has Unique solution and hence equations are consistent.

**Ques.5. **** **

**Ans. **Matrix form of given equations is AX = B

A =

= =

Now (adj. A) =

And (adj. A) B = = =

hance, given equations are inconsistent.

**Ques.6. **** **

**Ans. **Matrix form of given equations is AX = B

A =

=

There has Unique solution and hence equations are consistent.

**Ques.7. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

so, solution is unique and =

=

hance, and

**Ques.8. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

so, solution is unique and =

=

=

hance, and

**Ques.9. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

so, solution is unique and =

=

=

hance, and

**Ques.10. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

so, solution is unique and =

=

hance, and

**Ques.11. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

= =

so, solution is unique and =

=

=

hance, and

**Ques.12. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

=

so, solution is unique and =

=

=

hance, and

**Ques.13. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

=

so, solution is unique and =

=

=

hance, and

**Ques.14. **** **

**Ans. **Matrix form of given equations is AX = B

A = , X = and B =

=

=

so, solution is unique and =

=

=

hance, and

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

**Ans. **Given: Matrix A =

=

……….(i)

Now, and and

adj. A = =

From eq. (i),

=

Now, Matrix form of given equations is AX = B

Here A = , X = and B =

so, solution is unique and

=

=

hance, and

**Ques.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

A = , X = and B =

= =

so, solution is unique and = …….(i)

Now,

adj. A =

From eq. (i),

=

=

so, and

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

##### Other Pages of this Chapter: 4. Determinants

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