Need help : Rank of Determinant

[Mahmoud Ibrahim]

Please , I need help for the attached question . Thanks

[nathi123]

If rank of A is 2 , then the determinant of A must be equal to 0 ( det A = 0 ) Det A = 2.0.(-1) + 4.3.k+1.1.2 - 2.0.3 - 1.(-1).k-2.4.1=12k+2 - 8 +k =13k - 6
[tex]detA=0\Leftrightarrow k = \frac{6}{13}[/tex]

[Mahmoud Ibrahim]

Thanks very much.

[Guest]

Mat_Rank.png (7.28 KiB) Viewed 1717 times

Please. In this question, det(A)[tex]\ne[/tex] zero
And any minor determinant containing K not equal zero.
How can I find the real value of K ?
Thank you very much.

[Guest]

Note:
the second row = the first + 1.
As : the first column , 0 = -1 + 1 and in the third column 2 = 1 + 1
Is this means that in the second column K = 3 + 1 , then k = 4 ???
Is this answer correct ? If so , why the question said that R(A) = 3 ?.
In this case what we get from R(A) = 3 ??
Thank you again.