Расчетные задания (Кузнецов) / 10-Линейная алгебра

11.4.2x12 +9x22 +2x32 −4x1x2 +4x2 x3.

11.5.−4x12 −4x22 +2x32 −4x1x2 +8x1x3 −8x2 x3.

11.9.−x12 − x22 −3x32 −2x1x2 −6x1x3 +6x2 x3.

11.10.x12 −7x22 + x32 −4x1x2 −2x1x3 −4x2 x3.

11.16.−(12)x12 +5x22 −(12)x32 −4x1x2 +3x1x3 +4x2 x3.

11.17.x12 + x22 − x32 −4x1x3 +4x2 x3.

11.18.−2x12 +2x22 −2x32 +4x1x2 −6x1x3 +4x2 x3.

11.27.5x12 +13x22 +5x32 +4x1x2 +8x2 x3.

11.28.2x12 +2x22 +2x32 + 23 x1x2 + 4 32 x2 x3.

11.30.−2x12 +5x22 −2x32 +4x1x2 +4x2 x3.

11.31.−3x12 +9x22 +3x32 +2x1x2 +8x1x3 +4x2 x3.

Задача 12. Исследовать кривую второго порядка и построить ее.

12.1.−x2 − y2 +4xy +2x −4 y +1 = 0.

12.2.2x2 +2 y2 −2xy −2x −2 y +1 = 0.

12.3.4xy +4x −4 y = 0.

12.4.−2x2 −2 y2 +2xy −6x +6 y +3 = 0.

12.5.−3x2 −3y2 +4xy −6x +4 y +2 = 0.

12.6.−2xy −2x −2 y +1 = 0.

12.7.−x2 − y2 −4xy −4x −2 y +2 = 0.

12.8.−4x2 −4 y2 +2xy +10x −10 y +1 = 0.

12.9.4xy +4x −4 y −2 = 0.

12.10.x2 + y2 +2xy −8x −8y +1 = 0.

12.11.x2 + y2 + 4xy −8x −4 y +1 = 0.

12.12.x2 + y2 −2xy −2x +2 y −7 = 0.

12.13.2xy +2x +2 y −3 = 0.

12.14.4x2 +4 y2 +2xy +12x +12 y +1 = 0.

12.15.3x2 +3y2 +4xy +8x +12 y +1 = 0.

12.16.x2 + y2 −8xy −20x +20 y +1 = 0.

12.17.3x2 +3y2 −2xy −6x +2 y +1 = 0.

12.18.4xy +4x +4 y +1 = 0.

12.19.3x2 +3y2 −4xy +6x −4 y −7 = 0.

12.20.−4xy −4x +4 y +6 = 0.

12.21.5x2 +5y2 −2xy +10x −2 y +1 = 0.

12.22.2x2 +2 y2 +4xy +8x +8y +1 = 0.

12.23.−x2 − y2 +2xy +2x −2 y +1 = 0.

12.24.2x2 +2 y2 −4xy −8x +8 y +1 = 0.

12.25.3x2 +3y2 +2xy −12x −4 y +1 = 0.

12.26.−4xy +8x +8y +1 = 0.

12.27.2x2 +2 y2 −2xy +6x −6 y −6 = 0.

12.28.x2 + y2 +4xy +4x +2 y −5 = 0.

12.29.4xy +4x −4 y +4 = 0.

12.30.3x2 +3y2 −4xy +4x +4 y +1 = 0.

12.31.x2 + y2 −4xy +4x −2 y +1 = 0.