MATH 21B Midterm: MATH 21B Harvard 21b Spring 18Solution2
Document Summary
Review material for the final examination of math 21b. Formula for the inverse matrix of a 2 2 matrix with nonzero determinant. (7) the span of a set of vectors. Linear dependence and independence of a set of vectors. Dimension. (8) 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. The vector x and and its new coordinates ~y with respect to a basis ~v1, , ~vn are related by. A matrix a of a linear transformation t from rn to rn is related to the new matrix representing t with respect to ~v1, , ~vn by as = sb, because. ~vn b11 bn1 b1n bnn (14) concept of a linear space (also known as a vector space).
