Question

the rank of the matrix (123 246 369)​

Answer 1

Answer:

246,123 the rank of the matrix.

Answer 2

Given,

• The matrix $\left[\begin{array}{ccc}1&2&3\\2&4&6\\3&6&9\end{array}\right]$ is given.

To find,

• The rank of the given matrix.

Solution,

The rank of the matrix $\left[\begin{array}{ccc}1&2&3\\2&4&6\\3&6&9\end{array}\right]$ is 1.

The Rank of the matrix is defined as the minimum number of non-zero rows or columns present in the matrix. The rank of the matrix can find out by finding the non-zero determinant of all the submatrix of the given matrix.

            Let A = $\left[\begin{array}{ccc}1&2&3\\2&4&6\\3&6&9\end{array}\right]$

               Using $R_{2}$ → $R_{2}$ - 2$R_{1}$

                  A ≈ $\left[\begin{array}{ccc}1&2&3\\0&0&0\\3&6&9\end{array}\right]$

             Using$R_{3}$ → $R_{3} -3R_{1}$

                 A ≈ $\left[\begin{array}{ccc}1&2&3\\0&0&0\\0&0&0\end{array}\right]$

Since there is only 1 non-zero row in matrix A.

So, the rank of the matrix A is 1 i.e. ρ(A) = 1

Hence, the rank of the matrix $\left[\begin{array}{ccc}1&2&3\\2&4&6\\3&6&9\end{array}\right]$ is 1.