Question

under what condition the rank of matrix will be [(1 0 0) (0 k-2 2) (0 0 k+2) (0 0 3)]<3
please answer me immediately​

Answer 1

Answer:

I think I've got the right intuition here. Row reduce and then by the knowlege that the matrix has a rank of 2, I know the third row will be one of zeros. Therefore, for the third entry in that third row, I will likely have some constant added or subtracted from K, which can be set equal to zero.

I've row reduced down but I'm essentially at a point where I can't get a rational number for K. Hopefully this is purely a computational error but please let me know if I'm going wrong elsewhere.

Answer 2

Given, that the rank of the matrix $\left[\begin{array}{ccc}1&0&0\\0&k-2&2\\0&0&3\end{array}\right]$ is less than 3.

Solution,

For calculating the value of 'k' the determinant of the matrix should be equals to 0.

Therefore,

$\[\begin{array}{l}1\left\{ {3\left( {k + 2} \right) - 0} \right\} = 0\\ \Rightarrow 3k = - 6\\ \Rightarrow k = - 2\end{array}\]$

Hence, the value of k is 3.