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1. Wilo S or e in the space provided. 1. Write C or in the space provided. N__ O N__P(R) • ___Z V2__ R

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Trinidad Tremblay
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31 Jan 2018
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9. Let F = {0,1,} be a field with three elements. Write 0, 1 or I in the space provided: r² = _ 1+1=

(6] 8. Let V = P(R) be the vector space of polynomials of degree less than or equal to 2 with usual addition and scalar multiplication. Let W = R+ be the vector space of positive real numbers with vector addition defined by r + s = rs for all r,s EW, and scalar multiplication defined by cr = pl for all TEW,CER For the linear transformation T: V W where T(1+2) = 2, ,T(x2) = 1, T(1 – 1) = find T(a + box + cra).

4. (12 points) Let the matrix A and its reduced row echelon form R be given by the following. A= [ 1 -2 2 -3 1 -2 4 -1 4 1 -3] [1001 1] -4 0 0 1 0 1 1 7 -1 0 0 1 1 -1 | = R. (a) Find a basis for the column space of A. (b) Find a basis for the row space of A. (c) Find a basis for the null space of A. (d) Verify that the dimension of the column space of A plus the dimension of the null space of A is equal to the number of columns of A.

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