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Unformatted text preview: 2 + 9 x 3 =-6 Show all the computational steps of how you get the answer. * The real exam might be totally dierent !!! 1 5. Find the rank, the dimension and a basis of the column space of the matrix 1-4 9-7-1 2-4 1 5-6 10 7 . Show all the computational steps of how you get the answer. 6. Let v 1 ,v 2 ,v 3 ,v 4 R 4 . Suppose v 1 ,v 2 ,v 3 are linearly dependent. Show that v 1 ,v 2 ,v 3 ,v 4 must also be linearly dependent. 7. Let A,B R n n be such that AB is invertible. Show that A and B are both invertible. 8. Let A R n n be such that A 2 = 0. Show that all the eigenvalues of A are zero. 9. Let u,v R n . Show that if k u + v k 2 = k u k 2 + k v k 2 then u and v are orthogonal. 2...
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