## NCERT Solutions for Class 12 Maths Exercise 4.6 Chapter 4 Determinants – FREE PDF Download

NCERT Solutions for Class 12 Maths Chapter 4 – Determinants is a sure-shot way of obtaining the complete marks in the particular chapter for Board Exam 2019- 2020. CoolGyan provides you with Free PDF download of the same solved by Expert Teachers as per NCERT (CBSE) Book guidelines. They provide the students with precise and to the point answers which fetch very good marks in Board Exams. Download today the NCERT CBSE Solutions for Class 12 Maths Chapter 4 – Determinants to achieve your goal score. Class 12 Maths Chapter 4 – Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.

# NCERT Solutions for Class 12 Maths Chapter 4 – 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. x+3y=5 2x+6y=8x+3y=5 2x+6y=8

**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 =

|A|=∣∣∣5723∣∣∣|A|=|5273| =

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 =

= −20−(−9)=−20+9=−11≠0−20−(−9)=−20+9=−11≠0

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

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

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

**Ans.**Let Rs x, Rs y, Rs z 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 Rs. 5, Rs 8 and Rs 8 per kg.