Suppose a linear transformation TR3R3 is given Is the set S0

Suppose a linear transformation T:R³->R³ is given.

Is the set S₀ , consisting of all the vectors x in R³ for which T(x) = 7x, a vector subspace of R³ ? y/n

why?

Solution

T(X)=7X

this is a vector subspace of R^3

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Because X is a vector in R3 and T is Linear tranformation

T(X)=7X so 7X is also vector is R^3