Unformatted text preview: 0 0 0 0 0 0 0 0 . The ﬁrst and third columns of A are respectively a 1 = 2 1-3-1 and a 3 = -1 1-1-1 . a) Give the rank of the matrix A .  b) Give the dimension for each of the following subspaces row( A ), col( A ) and ker( A ).  c) Give a basis for each of the following subspaces row( A ), col( A ) and ker( A ).  4. Let A and B be two row-equivalent matrices. Are the column spaces of the two matrices necessarily the  same? If not, give a counter-example. [ /21]...
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- Spring '11
- Linear Algebra, Invertible matrix, following independent set, prof. Mike Newman