## equations

Noun

- plural form of
*equation*

- The adjoint determinant will be seen subsequently to present itself in the theory of linear
**equations**and in the theory of linear transformation. - Let there be 2n
**equations**r }}? - Linear
**Equations**.-It is of importance to study the application of the theory of determinants to the solution of a system of linear**equations**. - Suppose given the n
**equations**fl= = allxl +a12x2 + ï¿½ ï¿½ ï¿½ + annxn = 0, f2 =a21x1+a22x2+ï¿½ï¿½ï¿½+a2nxn =0, fn =anlxl +an2x2+ï¿½ï¿½ï¿½ +annxn = 0. - Denote by A the determinant (a11a22ï¿½ï¿½ï¿½ann)ï¿½ Multiplying the
**equations**by the minors A l, .., A2,,,,ï¿½ï¿½ï¿½Ani., respectively, and adding, we obtain x 1 (ai, Aig+a2p.A2lc+ï¿½ï¿½ï¿½+anï¿½Anï¿½) =xï¿½A=o, since from results already given the remaining coefficients of x 11' x 2, ...x ï¿½ 'i xï¿½+I,...x, vanish identically.

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- equations

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