# Exam1A - 1-1-1 1-4 2-8 1 3-1 4 Find the value(s of h for...

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M340L EXAM 1A SPRING, 2008 Dr. Schurle Your name: Your UTEID: 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. After many row operations you have changed the matrix A to the following. Describe all solutions of A x = 0 in parametric vector form. 1 - 2 3 1 4 0 0 1 0 3 0 0 0 1 2

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YOUR SCORE: 2. 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 EQUATION!!!! NaHCO 3 + H 3 C 6 H 5 O 7 Na 3 C 6 H 5 O 7 + H 2 O + CO 2 3. Do the columns of the following matrix span R 4 ? Show your work and explain your answer. 1 3 0 3 -

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Unformatted text preview: 1-1-1 1-4 2-8 1 3-1 4. Find the value(s) of h for which the following vectors are linearly dependent. Justify and explain your answer. 1-1-3 , -5 6 8 , 1 1 h 5. Suppose the vectors v 1 , v 2 ,..., v p are in R n and are linearly dependent . Suppose that T is a linear transformation from R n to R n . Show that the vectors T ( v 1 ) ,T ( v 2 ) ,...,T ( v p ) are also linearly dependent. 6. Let A = " 2 5-3 1 # and B = " 4-5 3 k # . Compute AB . 7. Suppose AB = AC , where B and C are n × p matrices and A is invertible. Show that B = C . Is this true in general when A is not invertible? Justify your answer....
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## This note was uploaded on 10/27/2008 for the course M 340L taught by Professor Pavlovic during the Fall '08 term at University of Texas.

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Exam1A - 1-1-1 1-4 2-8 1 3-1 4 Find the value(s of h for...

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