Question

Let a=<5,-3,0> and b=<1,-1,5>. Show that there are scalars s and t so that sa +tb =<-9,5,5>

Answer 1

Answer:

  s = -2

  t = 1

Step-by-step explanation:

If such scalars exist, they must be the solutions to the equations ...

  5s +t = -9

  -3s -t = 5

Adding these equations gives ...

  2s = -4

  s = -2

Filling in the first equation, we can solve for t:

  5(-2) +t = -9

  t = 1 . . . . add 10

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As a check on these values, we try them for all three vector components:

  -2<5, -3, 0> +1<1, -1, 5> = <-2(5)+1, -2(-3)-1, -2(0)+5> = <9, 5, 5>

as required.

The scalars s and t are (s, t) = (-2, 1).