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Khan Academy
Khan Academy: Linear Algebra: Determining Whether a Transformation Is Onto
Video reviews from previous videos that a function is invertible if and only if it is onto and one-to-one. Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the...
Khan Academy
Khan Academy: Linear Algebra: Relating Invertibility to Onto and One to One
Video first reviews that a function is invertible if and only if there is a unique solution to f(x) = y for any y. Extends this to show that a function is invertible if and only if it is surjective (onto) and injective (one-to-one). [6:31]
Khan Academy
Khan Academy: Linear Algebra: Surjective(onto), Injective(one to One) Functions
Video explains what a surjective or onto function is and also what an injective or one-to-one function is. Gives examples and non-examples of surjective and injective functions. [9:31]
Khan Academy
Khan Academy: Determining Whether a Transformation Is Onto
Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the co-domain.