Find the rank of the matrix A = \(\begin{pmatrix}4 & 5 & 2 & 2 \\3 &

1.	Find the rank of the matrix A = \(\begin{pmatrix}4 & 5 & 2 & 2 \\3 & 2 & 1 & 6\\4 & 4 & 8 & 0\end{pmatrix}\)
Answer» Given A = \(\begin{pmatrix}4 & 5 & 2 & 2 \\3 & 2 & 1 & 6\\4 & 4 & 8 & 0\end{pmatrix}\) order if A is 3 x 4.ρ(A) ≤ 3 Consider the third order minor, \(\begin{vmatrix}4 & 5 & 2 \\3 & 2 & 1 \\4 & 4 & 8\end{vmatrix}\) = 4(16 – 4) – 5(24 – 4) + 2 (12 – 8) = 48 – 100 + 8 = -44 ≠ 0 There is a minor of order 3 which is not zero. ρ(A) = 3

Find the rank of the matrix A = \(\begin{pmatrix}4 & 5 & 2 & 2 \\3 & 2 & 1 & 6\\4 & 4 & 8 & 0\end{pmatrix}\)

Answer»

Given A = \(\begin{pmatrix}4 & 5 & 2 & 2 \\3 & 2 & 1 & 6\\4 & 4 & 8 & 0\end{pmatrix}\)

order if A is 3 x 4.ρ(A) ≤ 3

Consider the third order minor,

\(\begin{vmatrix}4 & 5 & 2 \\3 & 2 & 1 \\4 & 4 & 8\end{vmatrix}\)

= 4(16 – 4) – 5(24 – 4) + 2 (12 – 8)

= 48 – 100 + 8

= -44 ≠ 0

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