MATH 21B Midterm: MATH 21B Harvard 21b Fall 07first Midterm review
Document Summary
Review for the first mid-term of math 21b. 2 2 matrix with nonzero determinant: the span of a set of vectors. Linear dependence and independence of a set of vectors. Dimension: determine the rank and the nullity of a matrix. Find a basis for the image and for the kernel of a matrix. Matrix of a linear transformation with respect to a basis. Relation of matrices of the same linear transformation with respect to two di erent bases. Similarity as an equivalence relation: concept a linear space (also known as a vector space). Addition and scalar multiplication in a linear space and the laws (associativity, com- mutativity, distributivity, etc. ) satis ed by them. Examples of linear spaces: solutions of di erential equations, spaces of polynomials, spaces of matrices, etc. The first midterm covers up to and including section 4. 1 of bretscher"s book on linear algebra with applications.
