Question

Determine whether the statements that follow are true or false, and justify your answer.

14: rank$\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 3& 6\end{array}\right|\mathbf{=}\mathbf{3}$

Short answer

True, rank of the given matrix is 3 because after finding the row echelon form there are three non-zero rows.

Step-by-step solution

Step 1:Rank of a matrix

For finding the rank of the matrix first of all we will change the given matrix in the echelon form.

We have given the matrix.

$\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 3& 6\end{array}\right|$

Justification of answer

Now, find the reduced row echelon form of the given system.