Question

线性代数求标准型参考答案上写的最后 +6X3^2不过,我计算后得出 最后+ 2X3^2请问,我算错了,还是参考答案给错了

Answer 1

是你算错了!

f = 2(x1)^2-2(x2)^2-4x1x3+8x2x3

= 2[(x1)^2-2x1x3+(x3)^2-(x3)^2]-2(x2)^2+8x2x3

= 2(x1-x3)^2-2[(x2)^2-4x2x3+(x3)^2]

= 2(x1-x3)^2-2(x2-2x3)^2+6(x3)^2