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. 
A = 
and B = 
= 
Therefore, Unique solution and hence equations are consistent.
2. 
A = 
and B = 
= 
Therefore, Unique solution and hence equations are consistent.
3. x+3y=5 2x+6y=8x+3y=5 2x+6y=8
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. 
Here A = 
= 
0
Therefore, Unique solution and hence equations are consistent.
5.
Here A = 
= 
= 
Now (adj. A) = 
And (adj. A) B = 
= 
= 
Therefore, given equations are inconsistent.
6.
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. 
Here A = 
, X = 
and B = 
|A|=∣∣∣5723∣∣∣|A|=|5273| = 
Therefore, solution is unique and 
= 
= 
Therefore, 
and 
8.
Here A = 
, X = and B = 
= 
Therefore, solution is unique and =
= 
= 
Therefore, 
and 
9.
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.
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. 
Here A = 
, X = 
and B = 
= 
= 
Therefore, solution is unique and =
= 
= 
Therefore, 
and 
12.
Here A = 
, X = and B = 
= 
= 
Therefore, solution is unique and =
= 
= 
Therefore, 
and 
13.
Here A = 
, X = and B = 
= 
= 
Therefore, solution is unique and =
= 
= 
Therefore, 
and 
14.
Here A = 
, X = and B = 
= 
= 
Therefore, solution is unique and =
= 
= 
Therefore, 
and 
15. If A = find Using solve the system of equations
find 
Using 
= 
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.
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.