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Let ๐‘ˆ=ย (2,ย 4,ย -5)ย ๐‘‰=(1,ย -6,9).ย ๐น๐‘–๐‘›๐‘‘ย 3๐‘ข-5๐‘ฃ

Question

Let ๐‘ˆ=ย (2,ย 4,ย -5)ย ๐‘‰=(1,ย -6,9).ย ๐น๐‘–๐‘›๐‘‘ย 3๐‘ข-5๐‘ฃ

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Solution

To find 3u - 5v, you need to multiply each vector by their respective scalar and then subtract the second vector from the first.

Step 1: Multiply vector U by 3 3U = 3*(2, 4, -5) = (6, 12, -15)

Step 2: Multiply vector V by 5 5V = 5*(1, -6, 9) = (5, -30, 45)

Step 3: Subtract 5V from 3U 3U - 5V = (6, 12, -15) - (5, -30, 45) = (1, 42, -60)

So, 3u - 5v = (1, 42, -60).

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