Finding the rank of a Matric: ( 1 n n ... n ( n 2 n ... n ( n 3 n ... n (............

[Xpertery]

Like the title says, find the rank of a Matric

( 1 n n ... n
( n 2 n ... n
( n 3 n ... n
(...............
( n n n ... n )


looks kinda weird, i know, but i don't know how to put horizontal and diagonal dots
Thanks

 

[Xpertery]

Finding the rank of a Matric

Please help solve the rank of the Matric below

1	n	n	...	n
n	2	n	...	n
n	n	3	...	n
...	...	...	...	...
n	n	n	...	n

 

[Harry_the_cat]

It'd have to be an nxn matrix, wouldn't it?

Edit. That's the dimensions not the rank

 

[Harry_the_cat]

Consider the cases where n=2, then n=3, then n=4. Can you generalise or see a pattern that might help you prove the general case?

 

[Xpertery]

it doesn't really say anything about the dimension of the matric.
i did try to consider when n=1 n=2 n=3 n=4 and etc. but i couldn't really put it in a way i can solve.
any help? T.T
Thanks for the reply

 

[HallsofIvy]

If nothing else, when looking at cases n= 1, 2, 3, 4, you should have seen that no row is linear combination of other rows.