writing this question in another form and showing that c is not equal to zero.

Question

Let A be an invertible $n \times n$ matrix with entries $a_{ij}$ . Suppose that for all $i \in \{1, 2, . . . , n\},$ $a_{i1} + a_{i2} + · · · + a_{in} = c.$

(1) Write the above equations in the form of $Av = w$. What are the vector $v$ and $w$? Is there any relation between vector $v$ and vector $w$?

(2) Show that $c$ is not equal to $0$.

Answer 1

Hint: Show that $(1,1,...,1)^T$ is an eigenvector with respect to the eigenvalue ...