Information about linear algebra proofs

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1) Let L:R^n -->R^n be a linear operator on R^n. suppose that L(x) = 0 for some x does not equal 0. Let A be the matrix representing L with respect to standard basis. Show that matrix A is singular.

2) True or false

a)every basis for R^n has n vectors for R^n?

b) A spanning set of vectors for R^n may have more than n vectors in it.

c)The size of the matrix A representing a linear transformation L: R^3 -->R^4 is 3x4

d)The transition matrix or change of basis matrix Se->f from basis E to basis F is always square and non-singular?

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