MAT 1341 Lecture Notes - Lecture 18: Invertible Matrix, Row And Column Spaces
19 Nov 2016
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Lecture 18: more on column space algorithm, null space, extending li sets, finding and extending bases. When we want to solve the following problem: So, we can remove the 2nd and 1st vector without changing the span. 16. 4 why does the column space algorithm work. Using this definition ^, we can easily check if a vector is in null(a) or not: This method is much easier than considering a spanning set and asking if a vector is a linear combination of two vectors in the spanning set. We can fortunately describe spans as null spaces: 16. 6 extending linearly independent sets to a basis of. So, a basis for the row space is . If we want to extend this basis of to a basis of , we have to add two more vectors. The easiest way is to add vectors where the 1 is in a column in which the rref didn"t have a leading 1.
