Khan Academy Static

We will define matrix-vector multiplication and think about the set of vectors that satisfy Ax=0 for a given matrix A (this is the null space of A). We then proceed to think about the linear combinations of the columns of a matrix (column space). Both of these ideas help us think the possible solutions to the Matrix-vector equation Ax=b.

6915_Showing_that_the_candidate_basis_does_span_C_A_.html

6909_Null_space_and_column_space_basis.html

6913_Dimension_of_the_column_space_or_rank.html

6914_Showing_relation_between_basis_cols_and_pivot_cols.html

6910_Visualizing_a_column_space_as_a_plane_in_R3.html

6905_Introduction_to_the_null_space_of_a_matrix.html

6907_Null_space_3_Relation_to_linear_independence.html

6912_Dimension_of_the_null_space_or_nullity.html

6906_Null_space_2_Calculating_the_null_space_of_a_matrix.html

6911_Proof_Any_subspace_basis_has_same_number_of_elements.html

6908_Column_space_of_a_matrix.html

6904_Matrix_vector_products.html