**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 A^{T} (read as A transpose).

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

**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 (A^{T} )^{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

x^{2} + 8 = 6x

x^{2} - 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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