Consider-the-system-of-equations-a-1-x-b-1-y-c-1-z-0-a-2-x-b-2-y-c-2-z-0-a-3-x-b-3-y-c-3-z-0-if-determinant-a-1-b-1-c-1-a-2-b-2-c-2-a-3-b-3-c-3-0-then-the-system-has-

Question Number 55843 by gunawan last updated on 05/Mar/19

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$${a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} {z}=\mathrm{0},\:{a}_{\mathrm{2}} {x}+{b}_{\mathrm{2}} {y}+{c}_{\mathrm{2}} {z}=\mathrm{0}\:, \\ $$$${a}_{\mathrm{3}} {x}+{b}_{\mathrm{3}} {y}+{c}_{\mathrm{3}} {z}=\mathrm{0}\:\:\mathrm{if} \\ $$$$\begin{vmatrix}{{a}_{\mathrm{1}} }&{{b}_{\mathrm{1}} }&{{c}_{\mathrm{1}} }\\{{a}_{\mathrm{2}} }&{{b}_{\mathrm{2}} }&{{c}_{\mathrm{2}} }\\{{a}_{\mathrm{3}} }&{{b}_{\mathrm{3}} }&{{c}_{\mathrm{3}} }\end{vmatrix}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{system}\:\mathrm{has} \\ $$

Commented by gunawan last updated on 05/Mar/19

$$\mathrm{What}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:{x}={y}={z}=\mathrm{0}\:? \\ $$

Answered by 121194 last updated on 05/Mar/19

$$\mathrm{the}\:\mathrm{system}\:\mathrm{was}\:\mathrm{infinite}\:\mathrm{solutions} \\ $$

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