Final Summer 2006 done

Final Summer 2006 done - Linear Algebra Mathematics 110.201...

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Unformatted text preview: Linear Algebra Mathematics 110.201 Summer 2006 Final Name: 1. There are 8 questions worth 200 points total 2. Do not open your booklet until told to begin. The exam will be 150 minutes long. 3. You may not use calculators, books, notes or any other paper. Write all your answers on this booklet. Additional paper is available if required. 4. You must show all your working and explain your answers clearly to obtain full credit! I, , will not discuss the contents of this exam with persons not present in this room before Thursday, August 3, 11:00 EST. Signature: 1 1. (25 pts) Consider the equations x + 2 y + 3 z = 4 x + ( k + 1) y + 4 z = 6 x + 2 y + ( k + 2) z = 6 For which values of k does this system have a unique solution? When is there no solution? When is there infinitely many? 2 2. (20 pts) Draw the image of the box [0 , 1] [0 , 1] under the transformation T : R 2 R 2 and describe the kernel and image (a) when T is a dilation (b) when T is a rotation (c) When T is a sheer (d) when...
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Final Summer 2006 done - Linear Algebra Mathematics 110.201...

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