Question

$\left[\begin{array}{cccc}1& 1& 1& 3\\ 2& 0& 4& 6\\ 1& 1& 3& 7\end{array}\right]$

a) What size is A?

b) What is the third column of A?

c) What is the second row of A?

d) What is the element of A in the (3, 2)th position?

e) What is role="math" localid="1668434071938" $A^T$?

Short answer

a) Size of A is$3\times 4$

b) Third column is$\left[\begin{array}{c}1\\ 4\\ 3\end{array}\right]$

c) Second row is$\left[\begin{array}{cccc}2& 0& 4& 6\end{array}\right]$

d) Element of A at (3,2) position is 1.

e) We get$A^T=\left[\begin{array}{ccc}1& 2& 1\\ 1& 0& 1\\ 1& 4& 3\\ 3& 6& 7\end{array}\right]$

Step-by-step solution

Step1:

a)

This is$3\times 4$ matrix

Count the number of rows followed by the number of columns.

Step 2:

b)

$\left[\begin{array}{c}1\\ 4\\ 3\end{array}\right]$

Enter the third column as a submatrix

Step3:

c)

$\left[\begin{array}{cccc}2& 0& 4& 6\end{array}\right]$

Enter the second column as a sub-matrix.

Step 4:

d)

Element in third row and second column is 1.

Step5:

e)

$A^T=\left[\begin{array}{ccc}1& 2& 1\\ 1& 0& 1\\ 1& 4& 3\\ 3& 6& 7\end{array}\right]$

Transpose of the matrix is obtained by interchanging columns and rows.