Home >All Categories > Science & Mathematics >Mathematics >Open Question aba Member since:October 19, 2007Total points:269 (Level 2)6. Let a : V ? W be a linear transformation. Show that if a is surjective and {v1, . . . , vn}
spans V , then {a(v1), . . . , a(vn)} spans W.
7. Let a : V ? W be a linear transformation. Show that if a is injective and {v1, . . . , vn}
is a linearly independent subset of V , then {a(v1), . . . , a(vn)} is a linearly independent
subset of W.
8. Let W be a finite dimensional subspace of V .
(a) Show that dimW <= dimV .
(b) Show that if dimW = dimV , then W = V .Answer Question

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