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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:
x1^2+5x2^2+x3^2+2x1x2+6x1x3+2x2x3=0 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 😉
x^2+3y^2+3z^2-2yz 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 $$\left(\tilde z^{2} \lambda_{3} + \left(\tilde x^{2} \lambda_{1} + \tilde y^{2} \lambda_{2}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$6 \tilde x^{2} + 3 \tilde y^{2} + 2 \tilde z^{2} = 0$$
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 $$\left(\tilde x1^{2} \lambda_{3} + \left(\tilde x2^{2} \lambda_{2} + \tilde x3^{2} \lambda_{1}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$- 3 \tilde x1^{2} - 2 \tilde x2^{2} + 6 \tilde x3^{2} = 0$$
then the canonical form of the equation will be $$\left(\tilde z^{2} \lambda_{3} + \left(\tilde x^{2} \lambda_{1} + \tilde y^{2} \lambda_{2}\right)\right) + \frac{I_{4}}{I_{3}} = 0$$ $$\tilde x^{2} - \frac{\tilde y^{2}}{2} - \frac{\tilde z^{2}}{2} = 0$$
Other calculators. Curvilinear integral; Canonical form of a curve; Surface defined parametrically; Surface defined by equation; The area beetween curves; Other languages: PT; Integral of / Double Integral / Reverse the order in the double integral. Reverse the order of the integration.