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

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

To disprove something, all you need is an example. Since there aren't many stipulations on this matrix, I can think of many singular nxn matrices that meet your criteria.

\(\displaystyle \begin{bmatrix}
a & a & b & \dots & \sum_{x=1}^{n}a_{1x}\\
a & a & c & & \\
a & a & d & & \vdots\\
a & a & e & \ddots & \\
a & a & f & & \sum_{x=1}^{n}a_{nx}
\end{bmatrix}\)

This matrix isn't invertible since column 1 and 2 are lin. dep.

\(\displaystyle \begin{bmatrix}
a & a & b & \dots & \sum_{x=1}^{n}a_{1x}\\
a & a & c & & \\
a & a & d & & \vdots\\
a & a & e & \ddots & \\
a & a & f & & \sum_{y=1}^{n}\sum_{x=1}^{n}a_{yx}
\end{bmatrix}\)

This matrix isn't invertible since column 1 and 2 are lin. dep.