Is k an Eigenvalue of A with Sum of Row Entries as k?

mjthiry
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1. Homework Statement

Suppose that A is a square matrix and the sum of the entries of each row is some number k. Is k an eigenvalue of A? if so, what is the corresponding Eigenvector?2. Homework Equations

Ax-λx=0
3. The Attempt at a Solution

(1-k)(K-λ)-k=0I am not sure how to solve this in a proof sense ( since we are not using specific numbers)
 
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Is there a vector can you multiply into A where the product will be (k, k, k, ..., k)T?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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