1. does the set of vectors span R 3. explain your answer
Solution
Any three noncoplanar vectors in R3 span R3
Equation of plane through 3 points is
Ax+bBy+Cz = 1
Now consider first three vectors
=> A+4B = 1
B+C = 1 => B = 1-C
-A+B+5C = 1
Substituting B = 1-C in 1st and 3rd equations we get 4C-A = 0 and 4C-A = 3
therefore no solution
=> these 3 vectors span R3
The last vector can be written as (-1/4)*V1+(-5/4)*V2+(1/4)*V3

2. Hence any three vectors can span R3