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jasenka [17]
2 years ago
5

Show that the transformation T defined byT(x1, x2) = (2x1 - 3x2, X1+4, 5x2) is not linear.​

Mathematics
1 answer:
erastovalidia [21]2 years ago
4 0

Let <em>u</em> = (1, 0) and <em>v</em> = (0, 1). Then

<em>T</em> (<em>u</em>) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)

<em>T</em> (<em>v</em>) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)

=>   <em>T</em> (<em>u</em>) + <em>T</em> (<em>v</em>) = (-1, 9, 5)

but

<em>T</em> (<em>u</em> + <em>v</em>) = <em>T</em> (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)

=>   <em>T</em> (<em>u</em> + <em>v</em>) ≠ <em>T</em> (<em>u</em>) + <em>T</em> (<em>v</em>)

which means <em>T</em> does not preserve addition, so it is not linear.

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Chance can wash the car in 2 hours, while Sandy can wash the same car in 4 hours. How many hours would it take for them to wash
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Answer:  First Option is correct.

Step-by-step explanation:

Since we have given that

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Number of hours Sandy can wash the car = 4 hours

Work done by Chance per hour is given by

\frac{1}{2}

Work done by Sandy per hour is given by

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Work done by altogether per hour is given by

\frac{1}{2}+\frac{1}{4}\\\\=\frac{2+1}{4}\\\\=\frac{3}{4}

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\frac{4}{3}

Hence, First Option is correct.

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<span><u>Answer </u>
18 feet and 4.5 inches

<u>Explanation </u>
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