Answer to Question #224602 in Linear Algebra for Anuj

Question

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

Answer 1

Given,

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

$\& k=3$

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

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

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

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