Question

The rank of the following matrix is-
[ 1 1 0
1 1 0
1 1 0 ]
1) 0 2) 1 3) 2 4) 3

Answer 1

1 is rank of this matrix

Answer 2

The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in its row echelon matrix and similarly for column echelon matrix. To find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.

Now, we have to find the rank of the matrix. So the matrix can be expressed as

$\left[\begin{array}{ccc}1&1&0\\1&1&0\\1&1&0\end{array}\right]$

= $\left[\begin{array}{ccc}1&0&0\\1&0&0\\1&0&0\end{array}\right]$

So, from this, we can find only 1 number of linear independent vector in the matrix after solving.

Answer: Rank of the matrix is 1.