2. 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-u² - 31v². (b) Q(u1, U2, U3) = 3u1 - 2u₁u2 + 4u₁u3 +5u²+ 4u3 - 2u₂u3. (c) For i = 1, 2,...,n with n nonzero constants or eigenvalues A₁, A2, ..., An analyse the sign values of X, for which the following quadratic form is PD or ND: Q(x1, x2,.. ‚Xn) = \₁x² + \₂x² + + Anx²2.

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