Question

The rank of the matrix \(A = \left[ {\begin{array}{*{20}{c}} 1&1&2\\ 1&2&3\\ 0&{ - 1}&1 \end{array}} \right]\)

Answer 1

Correct Answer - Option 4 : 3

Concept:

We know the property that the rank of a non-singular matrix (for which determinant ≠ 0) is its order.

Now, here determinant of matrix A is, |A| = 1(2 + 3) -1(1 - 0) + 2(-1 - 0) = 5 - 3 = 2

So, |A| ≠ 0

∴ Rank A = min(m, n)

m = n = 3

∴ Rank of A = 3