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

## 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:  Solution:    Question 2.
Find the rank of the folowing matrices by row reduction method: Solution:
(i) Let The last equivalent matrix is in row-echelon form. It has three non zero rows. So ρ(A) = 3
(ii) Let The last equivalent matrix is in row-echelon form. It has three non zero rows. ρ(A) = 3
(iii) Let 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: Solution:
(i) Let $$A=\left(\begin{array}{cc}{2} & {-1} \\ {5} & {-2}\end{array}\right)$$
Applying Gauss-Jordan method we get (ii) Let  (iii) Let   ### 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. Solution: A has at least one non-zero minor of order 2. $$\rho(\mathrm{A})$$ = 2

Question 2.
Find the rank of the following matrices. Solution: 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. Solution:  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 Solution:  Question 5.
Using elementary transformations find the inverse of the following matrices Solution: Question 6.
Using elementary transformations find the inverse of the following matrices Solution: Question 7.
Using elementary transformations, find the inverse of the following matrices Solution:  Question 8.
Using elementary transformations, find the inverse of the following matrices Solution:   Question 9.
Using elementary transformations, find the inverse of the following matrices Solution:  Question 10.
Using elementary transformations, find the inverse of the following matrices Solution: Since R2 has all numbers zero, Thus inverse of matrix A does not exist.