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 = 
= 
= 
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 = 
= 
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 
NCERT Solutions class 12 Maths Exercise 4.6
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 
NCERT Solutions class 12 Maths Exercise 4.6
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 
NCERT Solutions class 12 Maths Exercise 4.6
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
NCERT Solutions class 12 Maths Exercise 4.6
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, 
adj. A = 
From eq. (i),
= 
= 
Therefore, 
and 
Hence, the cost of onion, wheat and rice are ` 5, ` 8 and ` 8 per kg.