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Determinants Class 12 NCERT Solutions

NCERT Solutions Class 12 Mathematics Chapter 4 Determinants Download In Pdf

Chapter 4 Determinants Download in pdf

Chapter 4 Determinants

Download NCERT Solutions for Class 12 Mathematics

(Link of Pdf file is given below at the end of the Questions List)

In this pdf file you can see answers of following Questions

Evaluate the determinants in Exercises 1 and

Properties of Determinants

property of determinants and without expanding in Exercises

Determinant is a number associated to a square matrix

Area of a Triangle

MATHEMATICS

EXERCISE 4.3



Question 1. Find area of the triangle with vertices at the point given in each of the following :
(i) (1, 0), (6, 0), (4, 3)
(ii) (2, 7), (1, 1), (10, 8)
(iii) (–2, –3), (3, 2), (–1, –8)


Question 2. Show that points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.


Question 3. Find values of k if area of triangle is 4 sq. units and vertices are (i) (k, 0), (4, 0), (0, 2)
(ii) (–2, 0), (0, 4), (0, k)


Question 4. (i) Find equation of line joining (1, 2) and (3, 6) using determinants.
(ii) Find equation of line joining (3, 1) and (9, 3) using determinants.


Question 5. If area of triangle is 35 sq units with vertices (2, – 6), (5, 4) and (k, 4). Then k is (A) 12 (B) –2 (C) –12, –2 (D) 12, –2

Write Minors and Cofactors of the elements of following determinants

Find adjoint of each of the matrices in Exercises 1 and 2.

Applications of Determinants and Matrices

EXERCISE 4.6


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


Question 1. x + 2y = 2


Question 2. 2x – y = 5


Question 3. x + 3y = 5 2x + 3y = 3 x + y = 4 2x + 6y = 8


Question 4. x + y + z = 1


Question 5. 3x–y – 2z = 2


Question 6. 5x – y + 4z = 5 2x + 3y + 2z = 2 2y – z = –1 2x + 3y + 5z = 2 ax + ay + 2az = 4 3x – 5y = 3 5x – 2y + 6z = –1


Solve system of linear equations, using matrix method, in Exercises 7 to 14.


Question 7. 5x + 2y = 4


Question 8. 2x – y = –2


Question 9. 4x – 3y = 3 7x + 3y = 5 3x + 4y = 3 3x – 5y = 7


Question 10. 5x + 2y = 3


Question 11. 2x + y + z = 1


Question 12. x – y + z = 4 3x + 2y = 5 x – 2y – z = 3 2 2x + y – 3z = 0 3y – 5z = 9 x + y + z = 2


Question 13. 2x + 3y +3 z = 5


Question 14. x – y + 2z = 7 x – 2y + z = – 4 3x + 4y – 5z = – 5 3x – y – 2z = 3 2x – y + 3z = 12


Question 15. If A = 2 –3 5 3 2 –4 1 1 –2, find A–1. Using A–1 solve the system of equations 2x – 3y + 5z = 11 3x + 2y – 4z = – 5 x + y – 2z = – 3


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

real numbers, then the inverse of matrix

solutions

solutions


 


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