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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 

Question 10 worth 5 points Determine wheather or not the two given matrices are inverses of each other. Justify your answer. 

 Question 10 worth 10 points The management of a Rental Car company has allocated $840,000 to purchase 60 new automobiles to add to their existing fleet of rental cars. The company will choose from compact, mid-sized, and full-sized cars costing $10,000, $16,000 & $22,000, respectively. a.   Find formulas (linear equations) giving the options available to the company. b.   Could the company purchase 25 full-sized cars? Why? c.   Give one specific option of a car purchasing order (for the three different types of cars).

Question 6 worth  8 points Let :