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#ref #hw
1 yk what? we got this.
1.0.1 to review
- remember
- finite-dimensional!!
- find
- Find null space
- done!
- find column space / basis
- done!
- solving systems of equations?
- skip
- the inverse of a matrix is unique
- done!
- complex numbers using matrices
- done!
- proves
- Prove that any linear transformation can be represented by a matrix :: skip
- prove that the sum of subspaces A+B is a direct sum iff A intersect B = {0} :: done
- in a fin dim vec space, the len of any LID set is less than or equal to the len of any spanning set :: done
- if W1 and W2 are subspaces of a vec space V such that W1 union W2 is also a subspace, then one of the spaces is contained in the other :: done
- v1,…,vm is a list of vecs such that tv1,…,tvm is a LID in w. prove that v1,…,vm is LID. is converse true? :: done
- prove that a nonempty subset W of V is a subspace of V iff for each pair of vectors w1, w2 in W and each scalar c in F the vector cw1 + w2 in W. :: skip
- review
- linear dependence lemma
- done
- group
- done
- range
- done
- fundamental theorem
- done
- linear maps and basis of domain
- done
- linear maps can be uniqely defined by what they do to the basis
- questions
- span question
- done
- we can always remove u, and the list would be unchanged!