MATH307-Group Homework 9 Solved

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1.   Let e1 =  ,e2 =    , V = span(e1,e2 − e1),W = span(e2) be two

0  1 subspaces of C2, prove that C2 = V + W but it is not a direct sum.

2.   Let V = span{e1,e2},W = span{e2,e3}, where e1,e2,e3 are vectors in R3, prove R3 = V + W. Is the sum a direct sum? Justify your answer.

3.   Let A be a m × n complex valued matrix, use SVD to prove that Cm = range(A)⊕ null(A∗).