**Unformatted text preview: **A = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 . 4. Find a polynomial p of degree 3 that passes through the points (1 , 0), (-1 , 0) and has p (0) = 0. How many such polynomials are there. Sketch one of them. 5. Consider the linear system A~x = ~ b , where A = 1 a 1 2 b 1-2 c . For which choices of a,b,c does the system always have a unique solution. For the other choices of a,b,c give examples to show that the system may have either inﬁnitely many or no solutions. 6. Suppose that ~v 1 ,...,~v n are n vectors in R n . Prove the following theorem: If ~v i · ~v j = 0 for 1 ≤ i < j ≤ n , then { ~v 1 ,...,~v n } is linearly indepedent. 1...

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