Exam1B - 1 3 3-1-1-1 1-4 3-8 1 3-1 4 Find the value(s of h...

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M340L EXAM 1B 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 2 4 0 1 2 0 0 0 0 0 0 1
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YOUR SCORE: 2. Boron sulfide reacts violently with water to form boric acid and hydrogen sulfide (dou- ble 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 3. Do the columns of the following matrix span R 4 ? Show your work and explain your answer.
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Unformatted text preview: 1 3 3-1-1-1 1-4 3-8 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 , -7 8 6 , 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 BA . 7. Suppose BA = CA , 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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