Matrices And Eigen value Problems

Reduce the quadratic form 2xy+2x z-2yz to canonical form by orthogonal reduction. Also find its nature. Reduce the quadratic form x^2+5y^2+z^2+2xy+2yz+6zx to canonical form and hence find its rank.

Assignment II

1. Find the evolute of the parabola . 2. Find the evolute of the hyperbola . 3. A rectangular box open at the top , is to have a volume of 32cc. Find the dimensions of the box, that requires the least materials for its construction. 4. A rectangular box open at the top , is to have the capacity of 108 cu.ms. Find the dimensions of the box, requiring the least materials for its construction.