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Question 1 worth 6 points Determine which of the following sets is a subspace of  for an appropriate value of n. (i): All polynomials of degree exactly 4 with real coefficients (ii): All polynomials of degree 3 or less with nonnegative coefficients (iii): All polynomials of the form p(t) = a + bt2, where a and b are in

Question 9 worth 6 points Determine if the vector u is in the column space of matrix  A and whether it is in the null space of A. ,

Question 5 worth 8 points Given the set of vectors , determine whether the set of vectors is a basis for . Explain your reasoning.  

Question 4 worth 8 points Consider the polynomials: p1(t) = -t p2(t) = 2 + 2t p3(t) = -4 (i) Find a linear dependence relation among p1, p2, p3. (ii) Find a basis for Span {p1, p2, p3}. (iii) Use your answer from part (ii) to express v(t) = 6 + 4t  as a linear combination of vectors from the basis.    

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Question 3 worth 10 points Determine whether the given matrix A is diagonalizable. If it is, find an invertible matrix  such that 

Question 11 worth 10 points Given the below 2×2 linear system of equations: 

Question 5 worth 10 points Recall that   matrix  is similar to  matrix  if there is an invertible matrix  such that 

Question 1 worth 10 points Given A=[2341]            a.   Find matrices 

Question 9 worth 10 points Consider the subspace H of R3 that has the basis  a.   Find the xyz-equation that defines subspace . b.   Using the given basis , find an orthonormal basis for  (and verify!) c.   If