Let u=(2,6,-7), v=(-1,-1,8), and 3. If (2, 14, 11)=ku+lv what is the value of l?
Given,
u=(2,6−7) & v=(−1,−1,8)u=(2,6-7) \space \&\space v=(-1,-1,8)u=(2,6−7) & v=(−1,−1,8)
&k=3\& k=3&k=3
Also, (2,14,11)=ku+lvAlso,\space (2,14,11)=ku+lvAlso, (2,14,11)=ku+lv
=3(2,6,−7)+l(−1,−1,8)=3(2,6,-7)+l(-1,-1,8)=3(2,6,−7)+l(−1,−1,8)
(2,14,11)=(6−l,18−l,−21+8l)(2,14,11)=(6-l,18-l,-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)][l(a,b)k(c,d)=(la+kc,lb+kd)]
6−l=2 ⟹ l=4, also 18−l=14 ⟹ l=4also −21+8l=11 ⟹ l=4∴l=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=46−l=2⟹l=4, also 18−l=14⟹l=4also −21+8l=11⟹l=4∴l=4
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