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 

Question 12 worth 9 points An ice-cream shop sells only ice-cream sodas and milk shakes. It puts: 1 ounce of syrup and 4 ounces of ice-cream in an ice-cream soda 1 ounce of syrup and 3 ounces of ice-cream in a milk shake   If the store used 160 ounces of syrup and 512 ounces of ice-cream, how many ice-cream sodas and milk shakes did it sell? a)  Set up the system of equations, letting: x = # ice-cream sodas sold y = # milk shakes sold   b)  Solve the system (show your work and justify your answer).  

Question 6 worth  8 points Let :

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

Question 6 worth 10 points Orthogonally diagonalize the given symmetric matrix  by finding an orthogonal matrix  and diagonal matrix  such that 

Of the choices below, which is the best way to contact your instructor.