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在讲授完高中代数第二册“行列式和线性方程组”这一章后,我们给同学们留下这样一个题目:已知a,b,c是不全为零的三个实数,A,B,C是三个锐角,且它们满足下列关系式 a=bcosC+ccosB b=ccosA+acosC (M) c=acosB+bcosA 求证 A+B+C=π。有相当一部分同学不会解,我在改作业时发现有几个数学成绩优秀的学生是这样解的:把所给的关系式(M)看成关于cosA、cosB、cosC为未知数的三元线性方程组,则系数行列式
After teaching the chapter “Determinants and Linear Equations” in the second edition of the Algebra Algebra, we left the students with such a question: Know that a, b, c are three real numbers that are not all zero, A, B C is three acute angles, and they satisfy the following relation a=bcosC+ccosB b=ccosA+acosC (M) c=acosB+bcosA Proof A+B+C=π. A considerable number of classmates will not be able to solve. When I change my homework, I found that there are several excellent students with good mathematics. This is the solution: Consider the given relationship (M) as a ternary linearity with unknown cosA, cosB, and cosC. Equations, the coefficient determinants