# Thread: Linear algebra with matrices

1. ## Linear algebra with matrices

Hi I'm trying to work out this question - its in the matrices section. Any help would be appreciated! thanks.

2. Determine the values of x for which the system of equations below has a non-trivial solution:

xc
1 + c2 + c3 + c4 = 0
c1 + xc2 + c4 = 0
c1 + xc3 + c4 = 0
c1 + c2 + c3 + xc4 = 0

2. A homogenous system of equations has an infinite number of solutions if and only if the determinant of the coefficient matrix is 0.

Solve $\displaystyle \left|\begin{array}{cccc}x & 1 & 1 & 1 \\ 1 & x & 1 & 1\\ 1 & 1 & x & 1 \\ 1 & 1 & 1 & x\end{array}\right|= 0$

3. ah i was actually looking at something like this. However, would they all be 1's seeming that, for example, in the second and third equation c3 and c2 respectively are not involved. Why wouldnt it be more like:

x 1 1 1
1 x 0 1
1 0 x 1
1 1 1 x

?

Thanks

4. You are right. I misread your equations.

Try expanding by minors on the second row.

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