Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2

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Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2

Question 1.
Find the rank of the following matrices by the minor method:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q1
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q1.1
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q1.2
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q1.3
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q1.4

Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2

Question 2.
Find the rank of the folowing matrices by row reduction method:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q2
Solution:
(i) Let
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q2.1
The last equivalent matrix is in row-echelon form. It has three non zero rows. So ρ(A) = 3
(ii) Let
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q2.2
The last equivalent matrix is in row-echelon form. It has three non zero rows. ρ(A) = 3
(iii) Let
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q2.3
The last equivalent matrix is in row-echelon form. It has three non zero rows. ρ(A) = 3

Question 3.
Find the inverse of each of the following by Gauss-Jordan method:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q3
Solution:
(i) Let \(A=\left(\begin{array}{cc}{2} & {-1} \\ {5} & {-2}\end{array}\right)\)
Applying Gauss-Jordan method we get
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q3.1
(ii) Let
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q3.2
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q3.3
(iii) Let
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q3.4
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Q3.5

Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2

Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 Additional Problems

Question 1.
Find the rank of the following matrices. Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 1
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 2
A has at least one non-zero minor of order 2. \(\rho(\mathrm{A})\) = 2

Question 2.
Find the rank of the following matrices. Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 225
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 3
The last equivalent matrix is in the echelon form. It has three non-zero rows.
∴ \(\rho(\mathrm{A})\) = 3; Here A is of order 3 × 4

Question 3.
Find the rank of the following matrices. Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 4
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 452
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 5
The last equivalent matrix is in the echelon form. The number of non-zero rows in this matrix is two. A is a matrix of order 3 × 4. ∴ \(\rho(\mathrm{A})\) = 2

Question 4.
Using elementary transformations find the inverse of the following matrix Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 7
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 77

Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2

Question 5.
Using elementary transformations find the inverse of the following matrices Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 8
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 9

Question 6.
Using elementary transformations find the inverse of the following matrices Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 99
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 10

Question 7.
Using elementary transformations, find the inverse of the following matrices Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 100
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 11
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 12

Question 8.
Using elementary transformations, find the inverse of the following matrices Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 13
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 133
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 14

Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2

Question 9.
Using elementary transformations, find the inverse of the following matrices Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 144
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 15
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 16

Question 10.
Using elementary transformations, find the inverse of the following matrices Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 17
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.2 177
Since R2 has all numbers zero, Thus inverse of matrix A does not exist.

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