求二次型 ((x)_(1),(x)_(2),(x)_(3))=4({x)_(2)}^2-3({x)_(3)}^2+4(x)_(1)(x)_(2)-4(x)_(1)(x)_(3)+8(x)_(2)(x) 的标准形,-|||-并写出所作的可逆线性变换.

例4 判断二次型-|||-((x)_(1),(x)_(2),(x)_(3))=(x)_(1)^2+2(x)_(2)^2+4(x)_(3)^2+2(x)_(1)(

若二次型((x)_(1),(x)_(2),(x)_(3))=2({x)_(1)}^2+4({x)_(2)}^2+a({x)_(3)}^2+2b(x)_(1)(x

若二次型((x)_(1),(x)_(2),(x)_(3))=2({x)_(1)}^2+4({x)_(2)}^2+a({x)_(3)}^2+2b(x)_(1)(x

) (x)_(1)+4(x)_(2)-2(x)_(3)+8(x)_(4)=2 -(x)_(1)+2(x)_(2)+3(x)_(3)+4(x)_(4)=1 (x)

二次型f(x_(1),x_(2),x_(3))=x_(1)^2+4x_(2)^2+4x_(3)^2+2lambda x_(1)x_(2)-2x_(1)x_(3)

[题目]求一个正交变换 =(p)_(y), 把二次型f(x1,-|||-_(2),(x)_(3))=2({x)_(1)}^2+3({x)_(2)}^2+3(x)

矩阵（）是二次型({x)_(1)}^2+4(x)_(1)(x)_(2)+({x)_(2)}^2的矩阵A({x)_(1)}^2+4(x)_(1)(x)_(2)+(

已知实二次型f(x_(1)，x_(2)，x_(3))=x_(1)^2+4x_(2)^2+4x_(3)^2+2lambda x_(1)x_(2)-2x_(1)x_

10.对应二次型 ({x)_(1)}^2+4(x)_(1)(x)_(2)+3({x)_(2)}^2 的矩阵为 () .-|||-

求非齐次线性方程组 ) (x)_(1)+(x)_(2)-3(x)_(3)-(x)_(4)=1 3(x)_(1)-(x)_(2)-3(x)_(3)+4(x)_(