Proving Linearity of Matrix Operators: Is L(A)=2A a Linear Operator?

Dustinsfl
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L(A)=2A

My book doesn't have any examples of how to do this with matrices so I don't know how to approach this.
 
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Are you supposed to show that L is a linear operator? If so, just show that
1) L(A + B) = L(A) + L(B)
2) L(cA) = cL(A)

Here A and B are n x n matrices and c is a scalar.
 

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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