Math Problem Solver

The rank of the matrix is $2$.

The rank of a matrix is the dimension of the space spanned by its columns. The rank of a matrix is equal to the number of pivots in its row echelon form. Applying a sequence of elementary row operations to the original matrix transforms it to row echelon form: $$\begin{bmatrix}1 & 2 & 4 & 3\\ 0 & 0 & -2 & 2\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\end{bmatrix}$$ The row echelon matrix has $2$ pivots, therefore: $$\text{rank} = 2$$ The pivots of this matrix are located at positions: (1, 1), (2, 3)