In Exercises 39- 54, the reduced row echelon form of the a11gmemed mmrix of a sysrem of li11ear eq11ario11s is given. Determine whether this system of linear equations is consistent and. if so. find its geneml solwio11. /11 addition. in Exercises 47- 54, write the solution in vector form. 0 0 0 ]
M303 Section 4.5 Notes- The Dimension of a Vector Space 11-16-16 If is a vector space with 2 bas1s 2 , , is it true that they have the same number of elements o In notation, want to determine if #1 = # 2 o Note: for nonzero vector space, infinite number of bases exist (scalar multiples of basis are still bases) o For = ℝ , this is true; all bases must have elements (matrix must have vectors in ℝ ) to be linearly independent and span Theorem 9- If is a vector space and = , ,…, }is a basis with elements, then any set in with more than elements must be linearly dependent o Proof: Let {
