NCERT Solutions Class 12 Mathematics Chapter 4 Determinants Download In Pdf

Chapter 4 Determinants Download in pdf

**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

**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.

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- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 6 Application of Derivatives
- Chapter 7 Integral
- Chapter 8 Application of Integrals
- Chapter 9 Differential Equations
- Chapter 10 Vector Algebra
- Chapter 11 Three Dimensional Geometry
- Chapter 12 Linear Programming
- Chapter 13 Probability

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