Question #238795
Q=x1^2+3x2^2+3x3^2-2x2x3
1
Expert's answer
2021-09-21T00:27:36-0400

Q=(x1)2+3(x2)2+3(x3)22(x2)(x3)Q=(x1)2+2(x2)2+2(x3)2+(x2)2+(x3)22(x2)(x3)Q=(x1)2+2(x2)2+2(x3)2+(x2x3)2Q=[x1x2x3][x12x22x3]+[x2x3][x2x3]Q=(x_1)^2+3(x_2)^2+3(x_3)^2-2(x_2)(x_3)\\ Q=(x_1)^2+2(x_2)^2+2(x_3)^2+(x_2)^2+(x_3)^2-2(x_2)(x_3)\\ Q=(x_1)^2+2(x_2)^2+2(x_3)^2+(x_2-x_3)^2\\ Q= \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \begin{bmatrix} x_1 & 2x_2 & 2x_3\\ \end{bmatrix} +\begin{bmatrix} x_2-x_3 \end{bmatrix}\begin{bmatrix} x_2-x_3 \end{bmatrix}


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