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MATH 141: Linear Analysis I |
Fall 2019 |
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1. Consider the expression 4 |
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(a) Sketch a graphical representation of this expression using vectors.
(b) Describe in words what the scalars 4 and 2 represent in the sketch.
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Vectors ~v1, ~v2, and w~ are given in the picture below. Use graphical method only (drawing pictures), without any numerical calculation, to determine whether w~ a linear combination of ~v1 and ~v2. If not, why not? If yes, estimate the value of the scalars in front of ~v1 and ~v2 respectively.
3. Find the amount of gas used by each of the two cars. The first car gets 30 miles/gallon and the second
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car gets 21 miles/gallon. The total amount of gas used by both cars is 600 gallons and the total distance traveled by both cars is 16200 miles.
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Is it still possible to reach Old Man Gauss if you are given each of the following modes of transportation in stead of the hover board and magic carpet? Write a convincing argument that justify your conclusion. Use sentences, calculations, pictures, and anything that helps support your justification.
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only the hover board with velocity 31 miles/hour.
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only the magic carpet with velocity 12 miles/hour.
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(c) a hover board with velocity 1 miles/hour and a super hover board with with velocity 2 miles/hour. |
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miles/hour, a magic carpet with velocity |
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miles/hour, and a |
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(d) a hover board with velocity 1 |
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miles/hour. |
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broomstick with velocity 7 |
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is a linear combination of the vectors 2 |
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3. Detail |
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5. Determine whether the vector |
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your reasons. |
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