Matrices, System of Linear Equations, Gauss Elimination Method
Echelon Form, Elementary Matrices & Row Reduction
Determinant and its properties
Properties of determinants Interchange two rows or cols changes the sign: -> -1 * det(A) ... transpose -> det (A) unchanged. ... multiply row * k -> k * det(A) ... multiply matrix * k -> k^2 * det(A) ... det (A B) -> det(A) * det(B) ... proportional rows or columns -> det() == 0. ... Add multiple of one row to another -> det unchanged. ... Geometric interpretation.
Dimension of Vector Space
Image result for : Dimension of Vector Spacemath.stackexchange.com In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.