The rank of the matrix ⎡⎢⎣3−12−312−624⎤⎥⎦ is
The rank of a matrix is simply the maximum number of linearly independent vectors in a matrix. And this number is equal to the number of non-zero rows in its row echelon matrix. Therefore, 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. So, first step would be to convert the given matrix into row echelon form.
R2→R2+R1 and R3→R3+2R1
⎡⎢⎣3−12004008⎤⎥⎦
R1→R113, R2→R2(14) and R3→R3(18)
⎡⎢ ⎢⎣3−1323001001⎤⎥ ⎥⎦
R3→R3–R2
⎡⎢ ⎢⎣1−1323001000⎤⎥ ⎥⎦
∴ We have 2 non zero rows ⇒ Rank = 2.