link this set of equations to a single unknown

A=[a1 a2 a3 a4 0 0 0 0;a5 a6 a7 a8 0 0 0 0;0 0 0 0 a9 a10 a11 a12;0 0 0 0 a13 a14 a15 a16;a17 a18 a19 a20 a21 a22 a23 a24;a25 a26 a27 a28 a29 a30 a31 a32;a33 a34 a35 a36 a37 a38 a39 a40;a41 a42 a43 a44 a45 a46 a47 a48]

B=[C1;C2;C3;C4;C5;C6;C7;C8]

C=[0;0;0;0;0;0;0;0]

A*B=C

1- I want to take this determinant of A matrix and find its roots.

2- I wan to link this set of equations to a single unknown. ( like C1)

I'd be happy if you could help.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[John D'Errico]

Not gonna happen, well, not easily. For multiple reasons. You have a totally symbolic matrix A? Or are those all fixed numbers? Even so, there are still issues.

If the coefficientts in A are symbolic unknowns, then computing the symbolic determinant will be computational nightmare. And then solving for a zero will be analytically impossible in mathematics, due to the Abel-Ruffini theorem.

If the coefficients in A are real numbers, then using the determinant is just a bad idea, taught to you by a teacher who did not understand why it was bad, who was in turn taught by other teachers. It is a bad meme that will live on forever.

So if A is a real matrix, then use null. The solution is given by the function null, if any solution exists.

If you want that in turn to be parameterized by C1 in a symbolic form, then you want to learn about the mathematical solution, and what the output of null means. That in turn can turn into a small course on linear algebra, depending on what you know.