# HOW TO FIND THE TRANSPOSE OF THE MATRIX

How to Find the Transpose of the Matrix ?

Here we are going to see, how to find the transpose of the matrix.

Transpose of a matrix :

The matrix which is obtained by interchanging the elements in rows and columns of the given matrix A is called transpose of A and is denoted by AT (read as A transpose).

If order of A is m x n then order of AT is n x m . We note that (AT )T = A.

## How to Find the Transpose of the Matrix - Questions

Question 1 :

If A =

then find the transpose of a matrix.

Solution :

To find the transpose of the given matrix, we have to write the elements in the rows as columns and the elements in the columns as rows.

Question 2 :

If A =

then find the transpose of-A.

Solution :

Question 3 :

If A =

then verify (AT )T = A

Solution :

Hence proved.

Question 4 :

Solution :

Since the order of matrices are same, corresponding terms will be equal.

x = 3 , y = 12 and z = 3

Solution :

x + y  =  6  -----(1)

xy  =  8   ---(2)

5 + z  =  5

z =  5 - 5  =  0

From (2),

y = 8/x

By applying the value of y in (1), we get

x + (8/x)  =  6

x2 + 8  =  6x

x2 - 6x + 8  =  0

(x - 2)(x - 4)  =  0

x = 2 and x = 4.

Solution :

x + y + z = 9   ---(1)

x + z = 5   ---(2)

y + z  = 7   ---(3)

By applying (2) in (1), we get

y + 5  =  9

y = 9 - 5

y = 4

By applying the value of y in (3), we get

z = 7 - 4

z = 3

By applying the value of y and z in (1), we get

x + 4 + 3  =  9

x  =  9 - 7

x  =  2

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Transpose of the Matrix".

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