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## Homework Statement

Find the SVD of

## Homework Equations

## The Attempt at a Solution

I'm stuck

My question is why in the solution it originally finds u_2=[1/5,-2/5]' but then says u_2=[1/sqrt(5),-2/sqrt(5)]'. I don't see what math was done in the solution to change the denominator from 5 to square root 5.

**General Question**- When finding the singular value...

(sigma_1)^2 = constant, why do we only consider the positive root

sigma_1 = sqrt(constant)

because the solution to the problem is

sigma_1 = +/- sqrt(constant)

Thanks for any help you can provide me.