A nurse has provided teaching to her diabetic client. The nurse is trying to determine if learning has occurred. Which finding best indicates that learning has occurred?

Question 2 worth 8 points If the set is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space. is the set of all vectors of the form, where and are arbitrary real numbers.

Question 2 worth 8 points If the set is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space. is the set of all vectors of the form, where and are arbitrary real numbers.  

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

Question 2 worth 8 points If the set W is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space. is the set of all vectors of the form, where and are arbitrary real numbers.  

34. On examination, Mrs. Smith has a grade III/IV murmur. This means that the intensity is:

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

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