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

1.	Find the rank of the matrix A = \(\begin{pmatrix}-2 & 1 & 3 & 4 \\0 & 1 & 1 & 2\\1 & 3 & 4 & 7\end{pmatrix}\)
Answer» Given A = \(\begin{pmatrix}-2 & 1 & 3 & 4 \\0 & 1 & 1 & 2\\1 & 3 & 4 & 7\end{pmatrix}\) order of A is 3 x 4.So p(A) ≤ 3 Consider the third order minor \(\begin{vmatrix}-2 & 1 & 3 \\0 & 1 & 1 \\1 & 3 & 4\end{vmatrix}\) = -2(4 - 3) - 1(0 - 1) + 3(0 - 1) = -2 + 1 -3 = -4 ≠ 0 There exists a minor of order 3 which is not zero. So ρ(A) = 3

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

Answer»

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

order of A is 3 x 4.So p(A) ≤ 3

Consider the third order minor

\(\begin{vmatrix}-2 & 1 & 3 \\0 & 1 & 1 \\1 & 3 & 4\end{vmatrix}\)

= -2(4 - 3) - 1(0 - 1) + 3(0 - 1)

= -2 + 1 -3

= -4 ≠ 0

There exists a minor of order 3 which is not zero. So ρ(A) = 3