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3 years ago

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>

Mathematics

1 answer:

Vlad [161]3 years ago

5 0

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

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).

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