Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4

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Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4

Question 1.
Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)
Solution:
Area of triangle with vertices
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 1
∴ Area of A with vertices (0, 0), (1, 2) and (4, 3) is
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 2

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4

(as the area cannot be negative).

Question 2.
If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k.
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 3

Question 3.
Identify the singular and non-singular matrices:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 4
Solution:
(i) For a given square matrix A,
1. If |A| = 0 then it is a singular matrix.
2. If |A| ≠ 0 then it is a non singular matrix.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 5
⇒ A is a singular matrix.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 6
Which is a skew symmetric matrix
∴ |A| = 0 ⇒ A is a singular matrix.

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4

Question 4.
Determine the value of a and b so that the following matrices are singular:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 7
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 8
expanding along R1
b(4 + 4) + 7 (-6 – 1) = 0 (given)
8b + 7 (-7) = 0
(i.e.,) 8b – 49 = 0 ⇒ 8b = 49 ⇒ b = 49/8

Question 5.
If cos 2θ = 0, determine \(\left[\begin{array}{ccc}{\theta} & {\cos \theta} & {\sin \theta} \\ {\cos \theta} & {\sin \theta} & {0} \\ {\sin \theta} & {0} & {\cos \theta}\end{array}\right]^{2}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 9

Question 6.
Find the value of the product; Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 10
Sol:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 11
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 12

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 Additional Problems

Question 1.
Identify the singular and non-singular matrix.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 13
Solution:
If the determinant value of a square matrix is zero it is called a singular matrix. Otherwise it is non-singular.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 14

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4

Question 2.
Show that Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 15
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 16
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 17