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) (β2, β3), (3, 2), (β1, β8)

**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) (β2, 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, β 6), (5, 4) and (k, 4). Then k is
(A) 12 (B) β2 (C) β12, β2 (D) 12, β2

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

**Question 1.** x + 2y = 2

**Question 2. **2x β y = 5

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

**Question 4.** x + y + z = 1

**Question 5.** 3xβy β 2z = 2

**Question 6. **5x β y + 4z = 5
2x + 3y + 2z = 2 2y β z = β1 2x + 3y + 5z = 2
ax + ay + 2az = 4 3x β 5y = 3 5x β 2y + 6z = β1

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

**Question 7.** 5x + 2y = 4

**Question 8. **2x β y = β2

**Question 9.** 4x β 3y = 3
7x + 3y = 5 3x + 4y = 3 3x β 5y = 7

**Question 10.** 5x + 2y = 3

**Question 11. **2x + y + z = 1

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

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

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

**Question 15. **If A =
2 β3 5
3 2 β4
1 1 β2, find Aβ1. Using Aβ1 solve the system of equations
2x β 3y + 5z = 11
3x + 2y β 4z = β 5
x + y β 2z = β 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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