MIT
18 06 -
Lecture 8
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Lecture 8 A basic consists of vectors in the space Vectors independent The vectors span the space This means that nay v in R is a combination of basis vectors Three vectors in R do not form a basis because they are not independent Dimension of a space the number of vectors in any basis Smallest possible subspace the zero vector Its dimension is zero Its basis is the empty set meaning nothing at all Example Vector spaces is all 2x2 matrices The matrices are the vectors Find the basis The dimension is 4 Example What is the basis for the nullspace of R The basis for the null space is made up of the special solution vectors What is the dimension of the basis of the nullspace 3
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