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What can a canonical calculator do? For a given equation it finds: Canonical form of the equation (for lines and surfaces of second order) Basis-vector of canonical coordinate system (for 2nd order lines) Center of canonical coordinate system (for 2nd order lines) Detailed Solution in Two Ways:
2xy+2xz+2yz canonical form. The teacher will be very surprised to see your correct solution 😉
319 canonical form. The teacher will be very surprised to see your correct solution 😉
then the canonical form of the equation will be $$\left(\tilde z^{2} \lambda_{3} + \left(\tilde x^{2} \lambda_{1} + \tilde y^{2} \lambda_{2}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$- 2 \tilde x^{2} + 6 \tilde y^{2} + 6 \tilde z^{2} = 0$$
then the canonical form of the equation will be $$\left(\tilde x1^{2} \lambda_{3} + \left(\tilde x2^{2} \lambda_{2} + \tilde x3^{2} \lambda_{1}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$- \frac{\tilde x1^{2}}{2} - \frac{\tilde x2^{2}}{2} + \tilde x3^{2} = 0$$
then the canonical form of the equation will be $$\left(\tilde z^{2} \lambda_{3} + \left(\tilde x^{2} \lambda_{1} + \tilde y^{2} \lambda_{2}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$4 \tilde x^{2} + 2 \tilde y^{2} + \tilde z^{2} = 0$$
x^2+y^2+2xy*cos(a) canonical form. The teacher will be very surprised to see your correct solution 😉
6x^2+3y^2+14z^2+4xy+4yz+18zx canonical form. The teacher will be very surprised to see your correct solution 😉
then the canonical form of the equation will be $$\left(\tilde z^{2} \lambda_{3} + \left(\tilde x^{2} \lambda_{1} + \tilde y^{2} \lambda_{2}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$6 \tilde x^{2} + 3 \tilde y^{2} + 2 \tilde z^{2} = 0$$
xy+xz+yz canonical form. The teacher will be very surprised to see your correct solution 😉