# Exam1A - of the following matrix in terms of the parameters...

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M340L EXAM 1A 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 5 2 1 1 1 0 0 0 1 2 2 0 0 0 0 1 5 0 0 0 2 8 24

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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 - 2 8 1 0 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 - 5 3 1 6 2 3 17 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 3 2 1 b 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 1 2 3 + x 2 3 4-1 . (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) When an Alka-Seltzer tablet is dissolved in water, the following reaction takes place. Using the elements in order Na, H, C, O , write a vector equation whose solution can be used to balance the chemical equation. DO NOT SOLVE THE EQUA-TION!!!! NaHCO 3 + H 3 C 6 H 5 O 7 → Na 3 C 6 H 5 O 7 + H 2 O + CO 2...
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## This note was uploaded on 12/14/2009 for the course M 91795 taught by Professor Koch during the Spring '09 term at University of Texas.

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Exam1A - of the following matrix in terms of the parameters...

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