Linear Algebra and Its Applications · Problem 6.4.1

Computations with Matrices — Gilbert Strang

Mathematics · minimum-principles-quadratic

Problem

Consider the system Ax=bAx = b given by [2−10−12−10−12][x1x2x3]=[404].\begin{bmatrix} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 4 \\ 0 \\ 4 \end{bmatrix}. Construct the corresponding quadratic P(x1,x2,x3)P(x_1,x_2,x_3), compute its partial derivatives ∂P/∂xi\partial P/\partial x_i, and verify that they vanish exactly at the desired solution.

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