Find the rank of the matrix A = ((1, -3, 4, 7)(9, 1, 2, 2, 0))

Question

Find the rank of the matrix A = \( \begin{pmatrix} 1 & -3 & 4 & 7 \\ 9 & 1 & 2 & 0\\ \end{pmatrix} \) 

Answer 1

A = \( \begin{pmatrix} 1 & -3 & 4 & 7 \\ 9 & 1 & 2 & 0\\ \end{pmatrix} \)

Order of A is 2 × 4. So ρ(A) ≤ 2 

Consider the second-order minor

\(\begin{vmatrix} 1 & -3 \\ 9 & 1 \end{vmatrix}\)  = 1 + 27 = 28 ≠ 0

There is a minor of order 2 which is not zero. 

So ρ(A) = 2