Question

Hi.. Please help me with this problem of vectors and matrices.. the problem says: either a 3x3 matrix such that A(1 2 5) = (0 1 3) and A(2 3 -1)= (1 2 4) Calculate A(0 1 11)

Answer 1

You want to find some linear combination of the vectors (1,2,5) and (2,3,-1) that equals (0,1,11). If you can find that combination, you can write the vector (0,1,11) as:\[(0,1,11)=c_1(1,2,5)+c_2(2,3,-1)\]and what you want to figure out will become:\[A(0,1,11)=A(c_1(1,2,5)+c_2(2,3,-1))=c_1A(1,2,5)+c_2A(2,3,-1)\]\[=c_1(0,1,3)+c_2(1,2,4).\]Basically, if you can figure out c1 and c2, you are done.