Express each of the following quadratic forms as a matrix product involving a symmetric coefficient matrix. In addition, by using the principal minor theorem, classify each of the following quadratic forms. (a) Q(u,v)=8uv-u^(2)-31v^(2). (b) Q(u_(1),u_(2),u_(3))=3u_(1)^(2)-2u_(1)u_(2)+4u_(1)u_(3)+5u_(2)^(2)+4u_(3)^(2)-2u_(2)u_(3). (c) For i=1,2,dots,n with n nonzero constants or eigenvalues lambda_(1),lambda_(2),dots,lambda_(n) analyse the sign values of lambda_(i) for which the following quadratic form is PD or ND: Q(x_(1),x_(2),dots,x_(n))=lambda_(1)x_(1)^(2)+lambda_(2)x_(2)^(2)+dots+lambda_(n)x_(n)^(2)