Question

If $A=\left[\begin{array}{cccc}1& 0& 2& 3\\ 4& 2& 6& 4\end{array}\right]$, then find the fourth element of second column of $A^T.$

Answer 1

To obtain transpose of a matrix we need to convert all its rows into columns or all its columns into rows.

Given matrix is $A=\left[\begin{array}{cccc}1& 0& 2& 3\\ 4& 2& 6& 4\end{array}\right]$

Let’s convert all its rows into columns. It has two rows. So transpose will have two columns because columns of new matrix are nothing but rows of original matrix.

So column 1 of transpose = Row 1 of A

= 1

0

2

3

Similarly column 2 = 4

2

6

4

So $A^T=\left[\begin{array}{cc}1& 4\\ 0& 2\\ 2& 6\\ 3& 4\end{array}\right]$

Thus, fourth element of second column of this matrix is 4.