MathProblemsBank

5.1.6 Affine transformations

Problem: To obtain the canonical form of the hypersurface given by the equation \( 2 x_{1} x_{2}+2 x_{2}+x_{3}+1=0 \), it's necessary to move the origin of coordinates to the point \( (a, b, c) \), where \( a++b+c=\cdots \).