Is vector u = [3 3 2] is a linear combination of vector v1 =[1 0 1] and
vector v2 =[1 1 1] ?
could you please show me how to solve this problem? thank you very much.
Hello,
This question can be answered using the determinant the three vectors : is a linear combination of and iff the determinant equals 0. Do we have ?
Another way of answering this question is solving for . If this equation has at least one solution then is a linear combination of and . If it has no solution then...
In order for vector u = [3 3 2] to be a linear combination of vector v1 =[1 0 1] and vector v2 =[1 1 1], it would necessary u=3[1,1,1]+t[1,0,1]. That is the only way to have 3 in the second position of u. But that means that 3+t=3 and 3+t=2. But that is impossible.