Is T(x, y) = (x1+5, x2) a Linear Transformation?

joemama69
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Homework Statement



Verify the linear transformation & find the standard matrix A

T:R2->R2, T(x,y) = (x1+5,x2)

Homework Equations





The Attempt at a Solution



so i have to verify addition and multiplication

T(u+v) = ((u1+v1)+5,(u2+v2)
Does this fail.. it seems i will never be able to have the five on both sides where it looks like this... (u1+5,u2)+(v1+5,v2)

Did i do this correctly
 
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Yes. You have shown that it is not a linear transformation.
 

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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