Question 1 If u = <11,-5> and v = <-2,3> find 3u - 5v.

Question 2
If m = <0,0> and n = <1,-6> find m - n.

Explain how you got your answer.

Step-by-step explanation:

The answer is found by carrying out the indicated arithmetic. Multiplying a vector by a scalar multiplies each of the vector's components. Adding vectors adds corresponding components.

Question 1

  3u -5v = 3<11, -5> -5<-2, 3>

  = <3·11 -5(-2), 3(-5) -5(3)>

  = <33 +10, -15 -15>

  = <43 -30>

Question 2

  m - n = <0, 0> -<1, -6>

  = <0 -1, 0 -(-6)>

  = <-1, 6>

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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