Question #224602

Let u=(2,6,-7), v=(-1,-1,8), and 3. If (2, 14, 11)=ku+lv what is the value of l?


1
Expert's answer
2021-08-10T09:23:21-0400

Given,

u=(2,67) & v=(1,1,8)u=(2,6-7) \space \&\space v=(-1,-1,8)

&k=3\& k=3

Also, (2,14,11)=ku+lvAlso,\space (2,14,11)=ku+lv

=3(2,6,7)+l(1,1,8)=3(2,6,-7)+l(-1,-1,8)

(2,14,11)=(6l,18l,21+8l)(2,14,11)=(6-l,18-l,-21+8l) [l(a,b)k(c,d)=(la+kc,lb+kd)][l(a,b)k(c,d)=(la+kc,lb+kd)]

6l=2    l=4, also 18l=14    l=4also 21+8l=11    l=4l=46-l=2 \implies l=4,\\\space also \space 18-l=14\implies l=4\\also\space -21+8l=11\implies l=4\\\therefore l=4



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