Question

Q.3. Find the rank of the matrix = 1 2 3 1 4 2 2 6 5

Answer 1

The rank of the given matrix is 2.

Given : $\left[\begin{array}{ccc}1&2&3\\1&4&2\\2&6&5\end{array}\right]$

To find : Rank of the matrix
Solution:
Matrix  is an arrangement of elements, especially numbers, in a particular way. A matrix is a mathematical structure having rows and columns. The element aij of a matrix, say M refers to the element in the i-th row and j-th column.  

The matrices are represented as square or rectangular parenthesis or in boxes. The horizontal and vertical lines of the matrix are represented as rows and columns. The numbers in the matrices are called entries or elements.

Lets calculate it,

Here, ∣A∣=1−4+3=0

So, rank of matrix <3.
Now, we will reduce into Echelon form,

R 2 = R 2−4R 1

By reducing into simpler steps we will get,
$\left[\begin{array}{ccc}1&2&3\\0&1&2\\0&0&0\end{array}\right]$

​Here, there are 2 non-zero rows in the Echelon form of A.

Hence rank =2 of the given matrix.

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