问一个线性代数问题：X1 X2 X3是X*3+qx+p=0的解,则行列式 X1 X2 X3 X3 X1 X2 X2 X3 X1
问题描述：
问一个线性代数问题：X1 X2 X3是X*3+qx+p=0的解,则行列式 X1 X2 X3 X3 X1 X2 X2 X3 X1
这题答案是零,
答
x1 x2 x3 x3 x1 x2 x2 x3 x1c1+c2+c3x1+x2+x3 x2 x3 x1+x2+x3 x1 x2 x1+x2+x3 x3 x1r2-r1,r3-r1x1+x2+x3 x2 x3 0 x1-x2 x2-x3 0 x3-x2 x1-x3行列式= (x1+x2+x3)[(x1-x2)(x1-x3)-(x2-x3)(x2-x3)]= (x1+x2+x3)(x1^2 - ...