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Exam1B - of the following matrix in terms of the parameters...

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M340L EXAM 1B SPRING, 2009 Dr. Schurle Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (16 points) After many row operations you have changed the matrix A to the following, which is not yet in reduced echelon form. Describe all solutions of A x = 0 in parametric vector form. 1 7 1 2 1 1 0 0 1 0 2 2 0 0 0 0 1 5 0 0 2 0 6 14

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YOUR SCORE: /100 2. (14 points) Describe in detail the method used to determine whether p vectors in R q are linearly independent and explain why the method works. 3. (16 points) Do the columns of the following matrix span R 4 ? Show the work and state the fact that justifies your answer. 1 3 0 3 1 1 1 - 1 0 4 - 3 8 1 - 1 3 - 1
4. (16 points) For which value(s) of h is the following matrix invertible? Show the work and state the fact that justifies your answer. - 1 - 4 1 1 5 4 3 15 h 5. (14 points) Use a cofactor expansion (NOT a calculator) to compute the determinant

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Unformatted text preview: of the following matrix in terms of the parameters a , b , and c . Show your work and simplify your answer as much as possible. a 2 3 b 1-4 1 c 6. (12 points) Suppose T is a linear transformation from R 2 to R 3 for which T " x 1 x 2 #! = x 1 5 1 2 + x 2 1 3-1 . (a) Give a matrix A for which T ( x ) = A x . (b) Calculate and simplify T " 2 3 #! (c) Could the range of T be all of R 3 ? Why or why not? 7. (12 points) Boron sulﬁde reacts violently with water to form boric acid and hydrogen sulﬁde (double yuk!) according to the following reaction. Using the elements in order B, S, H, O , write a vector equation whose solution can be used to balance the chemical equation. DO NOT SOLVE THE EQUATION!!!! B 2 S 3 + H 2 O → H 3 BO 3 + H 2 S...
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