如果你也在线性代数linearalgebra这个学科遇到相关的难题，请随时添加vx号联系我们的代写客服。我们会为你提供专业的服务。 linearalgebra™长期致力于留学生网课服务，涵盖各个网络学科课程：金融学Finance，经济学Economics，数学Mathematics，会计Accounting，文学Literature，艺术Arts等等。除了网课全程托管外，linearalgebra™也可接受单独网课任务。无论遇到了什么网课困难，都能帮你完美解决！

0.37 Elimination of Several Unknown QuantitiesWe shall now consider an equation involving several unknown quantities and suppose it reduced to the normal form, _i.e._, its first member developed with respect to the unknown quantities, and its second member zero. Let us first concern ourselves with the problem of elimination. We can eliminate the unknown quantities either one by one or all at once.For instance, let\[\begin{split}\phi(x,y,z)&=axyz+bxyz^{\prime}+cxy^{ \prime}z+dxy^{\prime}z^{\prime} &+fx^{\prime}yz+gx^{\prime}yz^{\prime}+hx^{\prime}y^{\prime}z+kx^{ \prime}y^{\prime}z^{\prime}=0\end{split} \tag{5}\]be an equation involving three unknown quantities.We can eliminate \(z\) by considering it as the only unknown quantity, and we obtain as resultant\[(axy+cxy^{\prime}+fx^{\prime}y+hx^{\prime}y^{\prime})(bxy+dxy^{\prime}+gx^{ \prime}y+kx^{\prime}y^{\prime})=0\]or\[abxy+cdxy^{\prime}+fgx^{\prime}y+hkx^{\prime}y^{\prime}=0. \tag{6}\]If equation (5) is possible, equation (6) is possible as well; that is, it is verified by some values of \(x\) and \(y\). Accordingly we can eliminate \(y\) from the equation by considering it as the only unknown quantity, and we obtain as resultant\[(abx+fgx^{\prime})(cdx+hkx^{\prime})=0\]or\[abcdx+fghkx^{\prime}=0. \tag{7}\]If equation (5) is possible, equation (7) is also possible;. that is, it is verified by some values of \(x\). Hence we can eliminate \(x\) from it and obtain as the final resultant,\[abcd\cdot fghk=0\]which is a consequence of (5), independent of the unknown quantities. It is evident, by the principle of symmetry, that the same resultant would be obtained if we were to eliminate the unknown quantities in a different order. Moreover this result might have been foreseen, for since we have (SS0.28)\[abcdfghk

## 发表回复