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# s11week07 - Math 205 Spring 2011 Homework 7 due March 14...

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Unformatted text preview: Math 205, Spring 2011 Homework 7: due March 14 Chapter 4, Sections 6, 8 and 10 (Review, T/F Questions) Week 7: 4.6 Bases and Dimension 4.8 Row and Column Space 4.10 Invertible Matrices (Review) ———– 2 Bases and Dimension Our main objective is the definition of basis. Vectors vectorv 1 ,vectorv 2 , . . . ,vectorv k in a vector space V that are are both (1) a spanning set for V and (2) linearly independent are called a basis for V. So (1) vector i, vector j are a basis of R 2 ; and (2) { vector i, vector j, vector k } is a basis of R 3 . A vector space has many bases, but the main fact is that if vectorv 1 ,vectorv 2 , . . . ,vectorv k is a basis of V and vectorw 1 , vectorw 2 , . . . , vectorw j is a second basis of V, then the number of vectors is the same: k = j. The number of vectors in a basis of V is called the dimension of V . 3 We start with verifications of linear independence in subspaces of R n Example: Show that the vectors vectorv 1 = (1 , 1) vectorv 2 = (1 , − 1) are a basis of...
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s11week07 - Math 205 Spring 2011 Homework 7 due March 14...

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