Question

Find a combination x1w1+x2w2+x3w3 that gives the zero vector: w1=[1, 2, 3], w2=[4, 5, 6], w3=[7, 8, 9].

Answer 1

rewrite the statement in math form:
\[
x_1<1,2,3>+x_2<4,5,6>+x_3<7,8,9>=<0,0,0>\\
<x_1,2x_1,3x_1>+<4x_2,5x_2,6x_2>+<7x_3,8x_3,9x_3>=<0,0,0>\\
\implies x_1+4x_2+7x_3=0\\2x_1+5x_2+8x_3=0\\
{\rm and}\;\; 3x_1+6x_2+9x_3=0
\]
solve the three equations simultaneously

Answer 2

Thank you so much.