[简答题]判定以下二次型是不是正定二次型(需说明理由):(1)f(x1,x2,x3=2x21+2x1x2-2x1x3-6x22一4x2x3-x23;(2)f(x1,x2,x3=2x21+2x1x2+4x1x3+2x22+2x2x3+3x23;(3)f(x1,x2,x3=2x21+2x1x2-4x1x3+2x222x2x3+5x23;(4)f(x1,x2,x3=x21+4x1x2+2x1x3+4x22+4x2x3+x23;(5)f(x1,x2,x3)=x21-2x1x24x1x3+2x224x2x3+7x23;(6)f(x1,x2,x3,x4)=x21+x22+4x23+8x24+6x1x3+4x1x4-2x2x3+2x2x4+2x3x4;(7)f(x1,x2,x3,x4)=x212x1x2+4x1x3+2x1x4+3x22-6x2x3+9x-12x2x4+19x24.
[简答题]判定以下二次型是不是正定二次型(需说明理由):(1)f(x1,x2,x3=2x21+2x1x2-2x1x3-6x22一4x2x3-x23;(2)f(x1,x2,x3=2x21+2x1x2+4x1x3+2x22+2x2x3+3x23;(3)f(x1,x2,x3=2x21+2x1x2-4x1x3+2x222x2x3+5x23;(4)f(x1,x2,x3=x21+4x1x2+2x1x3+4x22+4x2x3+x23;(5)f(x1,x2,x3)=x21-2x1x24x1x3+2x224x2x3+7x23;(6)f(x1,x2,x3,x4)=x21+x22+4x23+8x24+6x1x3+4x1x4-2x2x3+2x2x4+2x3x4;(7)f(x1,x2,x3,x4)=x212x1x2+4x1x3+2x1x4+3x22-6x2x3+9x-12x2x4+19x24.
发布时间:2025-07-10 20:21:40