1. ## Linear Algebra Problem

I need to know if there is a way to solve:

v1 = a + d
v2 = a + j
v3 = g + d
v4 = g + j

With v1, v2, v3, v4 independent there are 4 unknowns. It appears the determinant is zero or sparse.

Thanks,
timeng

2. ## Re: Linear Algebra Problem

I have no idea what you mean here! Are the "four unknowns" a, d, g, and j? And $v_1$, $v_2$, $v_3$, and $v_4$ are constants? But what do you mean by "independent"? Are they vectors?

Yes, row-reducing leads to a matrix with last row all 0s. That gives $0= v_1- v_2- v_3+ v_4$. If $v_1+ v_4$ is not equal to $v_2+ v_3$ then there is no solution. If $v_1+ v_4= v_2+ v_3$ then there are an infinite number of solutions.

3. ## Re: Linear Algebra Problem

Thanks. I need to go and better describe the overall problem. Then, maybe a solution approach will become evident.