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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:

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 R_{2} has all numbers zero, Thus inverse of matrix A does not exist.