Question 1077010: Find (a)2v + u, (b)u -3v, and (c)5u - v in the equation of u = <0, -4>, v = <-2,-8> Thanks.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Part (a)
2v + u = 2*v + 1*u
2v + u = 2*< -2,-8 > + 1*< 0,-4 >
2v + u = < 2*(-2),2*(-8) > + < 1*0,1*(-4) >
2v + u = < -4,-16 > + < 0,-4 >
2v + u = < -4+0,-16+(-4) >
2v + u = < -4,-20 >
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Part (b)
u - 3v = 1*u + (-3)*v
u - 3v = 1*< 0,-4 > + (-3)*< -2,-8 >
u - 3v = < 1*0,1*(-4) > + < -3*(-2),-3*(-8) >
u - 3v = < 0,-4 > + < 6,24 >
u - 3v = < 0+6,-4+24 >
u - 3v = < 6,20 >
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Part (c)
5u - v = 5*u + (-1)*v
5u - v = 5*< 0,-4 > + (-1)*< -2,-8 >
5u - v = < 5*0,5*(-4) > + < (-1)*(-2),(-1)*(-8) >
5u - v = < 0,-20 > + < 2,8 >
5u - v = < 0+2,-20+8 >
5u - v = < 2,-12 >
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