Select from the following sets, theone(s) which are linearly independent, given

Question

Select from the following sets, theone(s) which are linearly independent, given that each set is asubset of vectors from a standard vector space. A
{ [-6,-8],    [-8,-7],    [-8,-8] } B
{ sin( 2 x ) ,   cos( 2 x ) ,    e3 x,    1,    3 x,   x2 } C
{ -4 x2+x+3,   -5 x-1,    -5} D
{ -1+x,    x2-x-2,   x2-1,   -2 x } None of the above Select from the following sets, theone(s) which are linearly independent, given that each set is asubset of vectors from a standard vector space. A
{ [-6,-8],    [-8,-7],    [-8,-8] } B
{ sin( 2 x ) ,   cos( 2 x ) ,    e3 x,    1,    3 x,   x2 } C
{ -4 x2+x+3,   -5 x-1,    -5} D
{ -1+x,    x2-x-2,   x2-1,   -2 x } None of the above A
{ [-6,-8],    [-8,-7],    [-8,-8] } B
{ sin( 2 x ) ,   cos( 2 x ) ,    e3 x,    1,    3 x,   x2 } C
{ -4 x2+x+3,   -5 x-1,    -5} D
{ -1+x,    x2-x-2,   x2-1,   -2 x } None of the above

Explanation / Answer

(b) consider the linear combination a sin 2x + bcos 2x + ce3x + d + e (3x) + f ( x2 ) =0 then the only way to maintain the equation while a , b , c, d, e , f , are scalars is all the scalars are zero. so, the vectors are linearly indendent

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