Question

If the entries in each column of a square matrix M add upto 1, then an eigen value of M is

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The correct option is D 1

Assume any matrix in which sum of elements of any column is 1 and then proceed. For example, A = $\left[\begin{array}{ccc}2& -1& 1\\ 3& 2& -1\\ -4& 0& 1\end{array}\right]$

Now we can find eigen values of A by using $|A-\lambda I|$ = 0 $\Rightarrow$ $\lambda$ = 1.

Note: If sum of the elements in each row/column of a square matrix is equal to $\alpha$ the $\alpha$ is an eigen value of that matrix.