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Solutions ⇒ Class 12th ⇒ Mathematics-I ⇒ 4. Determinants

# 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

CBSE board students who preparing for class 12 ncert solutions maths and Mathematics-I solved exercise chapter 4. Determinants available and this helps in upcoming exams 2023-2024.

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

• All Chapter review quick revision notes for chapter 4. Determinants Class 12
• NCERT Solutions And Textual questions Answers Class 12 Mathematics-I
• Extra NCERT Book questions Answers Class 12 Mathematics-I
• Importatnt key points with additional Assignment and questions bank solved.

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

## 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,

From eq. (i),

so,  and

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

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## Study Materials List:

##### Solutions ⇒ Class 12th ⇒ Mathematics-I
1. Relations and Functions
2. Inverse Trigonometric Functions
3. Matrices
4. Determinants
5. Continuity And Differentiability
6. Application of Derivatives

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