$\bar{1} $ $0m$ $1$ $0n$ $v$ $m-11$ $1$ $1$ 1 $v$ $2^{\right)}$ $4.$ Reduce the quadratic form $Q=3x^{2}+5y^{2}+3x^{2}-2xy-2yz+2xz$ to canonical form and hence find its nature, rank, index and signature. $5$ Reduce the quadratic form $0-x$ $2+2\times 2$ to canonical form and bence find its nature

EXERCISE $24$ Reduce the quadratic form $2$ $2$ $2$ $2x_{1}+5x_{2}+3x_{3}+4x_{1}x_{2}$ to canonical form by an orthogonal transformation. $Als0$ find the rank, index, signature and nature of the quadratic form. [AU JAN $12$ JUN '10]

Reduce the following quadratic forms to canonical forms by orthogonal reduction $3x^{2}+5x^{2}+3x^{2}$ $1$ $2$ $3$ $-2x2^{x}3+2x_{3}x1-2x{1_{2}}^{x}$ $A|sO$ Find Index, Signature, Rank and nature of quadratic forms.