Determine if the vectors v1 = (2, −1, 2, 3), v2 = (1, 2, 5, −1), v3 = (7, −1, 5, 8) are linearly independent vectors in r4 .

Vectors are linearly independent if there doesn't exist a non-trivial linear combination which returns the zero vector. So, we must see if we can find three coefficients such that

. We have

So,

This linear combination returns the zero vector if

This system admits the only trivial solution a=b=c=0, so the vectors are linearly independent.

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.