Question

The vector[13,-15] is a linear combination of the vectors [1,5] and [3,c].
Find c.

Answer 1

should be [1,5] + k [3,c] = [13,-15]

Answer 2

5+c=-15

Answer 3

find the value of k by comparison, from first coordinate. and compare second coordinate and find c

Answer 4

c=-20

Answer 5

i got k=10, c=-65 0.0"

Answer 6

solve this equations:
5+kc =-15 and 1+3k = 13

Answer 7

k= 4, c = -5

Answer 8

why can't i put k to the other two? i got different numbers

Answer 9

damn how could mertz get a different no??

Answer 10

no thinking, just typing:)

Answer 11

mertz wanted to say 5k+c=-15

Answer 12

i guess, but he continued with this misstype

Answer 13

i set k[1,5]+[3,c]=[13,-15] .... c=-65
and [1,5]+[3,c]=k[13,-15] .....c=125/13

Answer 14

i think k is 4 and c is -5

Answer 15

bouth are correct i think...

Answer 16

i got same as myko

Answer 17

loook at my other two settings

Answer 18

why can't i do that?

Answer 19

good question...

Answer 20

if you look at it this way, maybe it's more clear:
(13,-15)-(1,5) =k(3,c)

Answer 21

=v="
what i concluded is [3,c] vector is the only vector that can be change since other two vectors are constant.

Answer 22

give me Medal =v="

Answer 23

not realy, becouse it says linear combo, so multiples of this vectors. Just there would be no way solution if we try to find it changing bouth at the same time. So we fix one and find the other... The question is way choosing different vector to keep it fixed different solutions come out

Answer 24

i only put one k on each equaltion i made. look at them.

Answer 25

a(1,5)+b(3,c) = (13,-15)
so...
a/b(1,5) +(3,c) =(13,-15)/b
or
(1,5) +b/a(3,c) = (13,-15)/a

so if you take a =1 everything is ok, ho ho ho

Answer 26

3k + 1 = 13
-> k = 12/3 = 4

5 + 4c = -15
=> c = -20/4 = -5

Answer 27

fine~

Answer 28

c= -20

Answer 29

two vector addition u + v= <1,5> + < 3,c> = <13, -15>...solve fr c.