Rank Revisited: Line and Column

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Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Explores matrix rank and vector space inclusion through elementary row operations.

Explains how to calculate the dimension of a kernel of a matrix transpose.

Explores matrix representations of linear maps and their invariance, using examples and special cases.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explores matrix equations, solutions, properties, and vector spaces in linear algebra.

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Explores changing bases in vector spaces and matrix representation of linear transformations.