Question

Find the rank of the matrix A= [012]
[123]
[321]

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Answer 1

Answer:

Step-by-step explanation: Given

$A=\left[\begin{array}{ccc}0&1&2\\1&2&3\\3&2&1\end{array}\right]$

Let's find the determinant of matrix

|A| = 0(2 - 6) - 1(1 - 9) + 2(2 - 6) = 8 - 8 = 0

Since determinant is 0 so the rank must be less than 3. Now consider minor of the matrix A

$A_{1} =\left[\begin{array}{ccc}0&1\\1&2\end{array}\right]$

Now,

|A1| = 0 - 1 = -1, which is non zero. Hence, the rank of (A) = 2