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Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).Let V be a ?nite dimensional linear space with a basis B. Let T : V ? V be a linear transformation. (a) Prove (f1, . . . , fm) is a basis for ker(T) if and only if ([f1]B, . . . , [fm]B) is a basis for ker([T]B). Conclude that nullity(T) = nullity([T]B).

Tutor Gautham Shiyakino

The f_i are linearly independent if and only if the [f_i]_B are linearly independ...

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