Find the rank of the matrix A = \( \begin{pmatrix} 1 & -3 & 4 & 7 \\

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

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

Answer»

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