Question 3 worth 6 points Suppose that 

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 1 worth 6 points Let H be the set of all polynomials of the form p(t) = a + bt3 where a and b are in .  Determine whether H is a vector space. If it is not a vector space, mention at least one reason why.

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 4 worth 8 points Consider the polynomials: p1(t) = 2 + t p2(t) = -2t p3(t) = 1 (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.    

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.    

Have you read the Course syllabus?

Question 4 worth 10 points Consider the probability matrix , where 

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

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