MATH 21 Study Guide - Final Guide: Linear Combination, Augmented Matrix, Row And Column Spaces
Document Summary
Winter 2012: true/false: (a) if the vectors {v1, v2, v3, v4} span r3, then {v1, v2, v3} is a basis of r3. The rst three vectors could be linearly dependent. 1 (b) if the rank of a 7 10 matrix a is 4, then the nullspace of a must be six dimensional. The zero matrix doesn"t belong to v . (d) if the rank of a 9 10 matrix is 5, then its nullspace is 4-dimensional. The nullspace has dimension 10 5 = 5. (e) there is an invertible 3 3 matrix a such that a2 is the zero matrix. |a|2 = |a2| = |zero matrix| = 0 implies that a is singular: for each of the matrices a and b, nd the determinant, the rank, a basis of the nullspace, and a basis of the row space. Is a basis of the row space of.
