MAT2705-02/06 09F Test 2 Print Name (Last, First) _________________________________|__
Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC). You may use technology for row reductions, determinants and matrix inverses.
1. a) On the grid to the right, draw in arrows representing the vectors 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbW92ZXJHRiQ2JS1GIzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y7USdub3JtYWxGJ0ZDLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRjQ2I1EhRidGQy1JI21vR0YkNi5RLSZSaWdodEFycm93O0YnLyUscGxhY2Vob2xkZXJHRjlGQy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGUy8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0ZTLyUobGFyZ2VvcEdGUy8lLm1vdmFibGVsaW1pdHNHRlMvJSdhY2NlbnRHRlMvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zcby9GaW5GOS1GTDYtUSI9RidGQy9GUlEmZmFsc2VGJy9GVUZkby9GV0Zkby9GWUZkby9GZW5GZG8vRmduRmRvL0ZpbkZkby9GW29RLDAuMjc3Nzc3OGVtRicvRl5vRlxwLUZMNi1RIn5GJ0ZDRmNvRmVvRmZvRmdvRmhvRmlvRmpvRmpuRl1vLUkobWZlbmNlZEdGJDYmLUYjNictRkw2LVEqJnVtaW51czA7RidGQ0Zjb0Zlb0Zmb0Znb0Zob0Zpb0Zqby9GW29RLDAuMjIyMjIyMmVtRicvRl5vRmpwLUZANiRRIjFGJ0ZDLUZMNi1RIixGJ0ZDRmNvL0ZVRjlGZm9GZ29GaG9GaW9Gam9Gam4vRl5vUSwwLjMzMzMzMzNlbUYnRlxxRkNGQy8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGQw== and 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. Then draw in the parallelogram that graphically expresses 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 as a linear combination of 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.
From the grid, read off the coordinates 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of 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 with respect to these two vectors and express 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 as a linear combination of them. Explain how you got these numbers.b) Now write down the matrix equation that enables you to express 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 as a linear combination of the other two vectors, solve that system using matrix methods, and then express 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 explicitly as a linear combination of those vectors.
c) Check your linear combination by expanding it out to get the original vector. Did you?
d) Does your matrix result agree with part a)?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
2. a) For 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 with , 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,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, 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 and 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, solve the equations 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, writing down the augmented matrix and its RREF form, identifying Leading and Free variables, and stating your result for 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.
b) From your general solution write down a basis 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 of the solution space.c) There is one independent relationship among these 4 vectors. Write down a single linear combination of these vectors equal to the zero vector and solve it for the last vector which enters the relationship. What are the remaining vectors of the set? Do these form a basis of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiNRIUYnRj4= ? Explain why or why not.3. a) Can 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 be expressed in terms of 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? If so, do so and check that your expression reduces to 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 If not explain why not. Show all work to support your claim.solution1. combining vectors in the planeb)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic=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)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSNiMUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GMzYtUSIrRidGL0Y2RjlGO0Y9Rj9GQUZDL0ZGUSwwLjIyMjIyMjJlbUYnL0ZJRlctRiw2JFEiNEYnRi9GMi1GSzYlUSNiMkYnRk5GUQ==a)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ=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The sides are respectively twice and 4 times the basis vectors, so the coordinates are (2,4).2. linear relationships among 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a)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b) The single linear relationship is: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
so solving for the last vector in it we get
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 the remaining vectors are the first, second and fourth vectors. They are linearly independent since they do not satisfy any linear relationship, and hence they span the space and are a basis of the space.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. 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pledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet in on top of your answer sheets as a cover page, with the first test page facing up:"During this examination, all work has been my own. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: TTdSMApJNlJUQUJMRV9TQVZFLzE1MDc4MzQ2OFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiJCIiIzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyMDE0NFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyEiIiIiIjYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIxOTI1MlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyUiIyIjIiIkIiIjISIiIiIiNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyMjIzNlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiIyIiKTYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIzODc4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIywmJiUieUc2IyIiIiIiJCZGKTYjIiIjISIiLCZGKEYvRi1GKzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIzODk1MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiIyIiKTYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIzOTEyNFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyUiIyIjIyIiIiIiJiMhIiNGKUYnIyIiJEYpNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI1NTYyNFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyYlInlHNiMiIiImRig2IyIiIzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI1NTY5NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiIyIiJTYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI1NTc5NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiIyIiKTYi