线性代数的题,如图所示。请问如何用配方法把这个二次型化为标准形?

要详细过程,谢谢!
2024-11-07 13:41:04
推荐回答(1个)
回答(1):

f = 5[(x1)^2+(14/5)x1x2+(4/5)x1x3] + 5(x2)^2 - 4(x3)^2 - 4x2x3
= 5[x1+(7/5)x2+(2/5)x3]^2 - (24/5)(x2)^2 - (36/5)(x3)^2 - 4x2x3
= 5[x1+(7/5)x2+(2/5)x3]^2 - (24/5)[x2+(5/12)x3]^2 - (191/30)(x3)^2
= 5(y1)^2 - (24/5)(y2)^2 - (191/30)(y3)^2