# Tagged Questions

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### Can we say that there exist an integer n such $A+nB$ invertible?

If $A$ and $B$ are $3\times 3$ matrices and $A$ is invertible, then can we say that there exist an integer $n$ such that $A+nB$ invertible? I was trying by choosing n such that eigne values of $A+nB$ ...
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### $A$ be a $10\times 10$ matrix in which each row has exactly one entry equal to 1. find the possible value of the determinant

Let $A$ be a $10\times 10$ matrix in which each row has exactly one entry equal to $1$. And remaining nine entries of the row being $0$. Which of the following is not a possible value of the ...
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### Linear Algebra - Finding Eigenvalues of a Matrix

$A=\begin{bmatrix}3 & -2 & 5\\ 1 & 0 & 7\\ 0 & 0 & 2\end{bmatrix}$, Find the eigenvalues of A. I realized that if I swap columns I and II then I can make it an upper ...
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### Proving that an $n\times n$ matrix has at most $n$ distinct eigenvalues

$A$ is a $n\times n$ matrix over the field $F$. How can I prove that there are at most $n$ distinct scalars $c$ in $F$ such that $\det(cI - A) = 0$? Thank you!