Video first reviews what the null space is and how to solve for it using reduced row echelon form. Shows that any solution to the inhomogeneous system Ax = b will be the sum of a particular solution and a homogeneous solution. Extends this to show that for the transformation to be one-to-one the null space must only contain the zero vector which means the column vectors of the transformation matrix are linearly independent and a basis for the column space. Shows that if a linear transformation is one-to-one, then the rank of the transformation matrix is equal to its number of columns. This video also appears in the strand Algebra: Matrices. [19:59]
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