can someone please give me an example of an n x n matrix, where the last column is the sum of the previous n-1 columns?
i have to prove whether it is invertible or not
If they have to be, then yes. By last column, do you mean every column needs to be the sum? I thought you mean column n is the sum of all the columns.
It doesn't change anything then because column 2 is the sum of column 1 then; thus, column 1 and 2 are lin. ind.
Does that mean the nth column is the sum or does that mean column two is the sum of column 1, column 3 is the sum of column 1 and 2....? If the second is the case, you can make the matrix columns the Fibonacci numbers.
1, 1, 2, 3, 5, 8, ....
*note means a column vector of the nxn matrix
If you make a column vector of all 1s, then = , = , = ,....