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MTH 017

Linear Algebra for Mathematical Sciences

3. Let T: Rn → Rm be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in Rn. Prove that the set {T(v1), T(v2), T(v3)} is linearly dependent.

4. Let T:R3 → R3 be a linear transformation that reflects each vector (x1, x2, x3) through theplane x3=0 onto T(x) (x1, x2,-x3). Show that T is a linear transformation.