MATH-205 Midterm: Bates MATH 205 100705jayawant205exam
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Name: check that you have 7 questions on two pages, show all your work to receive full credit for a problem, (10 points) (for this problem do all calculations by hand. ) Determine all possible values of h and k such that the solution set of the following system (a) is empty (b) contains in nitely many solutions. 4x1 + 3x2 = k: (8 points) let a = [~a1 ~a2 ~a3 ~a4] be a 3 4 matrix. Explain. (b) write the vector ~a4 as a linear combination of the vectors ~a1, ~a2, and ~a3: (8 points) let t : r3 r2 be a linear transformation such that t (x1, x2, x3) = ( 2x2 + Explain: (6 points) suppose a 4 4 matrix a is invertible. A span r4. (if you nd it helpful, you may use the following steps in your explanation. ) So the number of pivots in a is.
