<p><ahref='https://en.wikipedia.org/wiki/linear algebra'title='wp:线性代数'>在线性代数中</a>,<ahref='https://en.wikipedia.org/wiki/Cramer's rule'title='wp:Cramer的规则'>Cramer规则</a>是一个<ahref='https://en.wikipedia.org/wiki/system of linear equations'title='wp:线性方程组'>线性方程组</a>解的显式公式,其中包含与未知数一样多的方程,只要系统具有唯一解,就有效。它通过用方程右边的矢量替换一列来表示(方形)系数矩阵的决定因素和从它获得的矩阵的解决方案。 </p><p>特定</p><p><big></big></p><p><big>$ \ left \ {\ begin {matrix} a_1x + b_1y + c_1z&= {\ color {red} d_1} \\ a_2x + b_2y + c_2z&= {\ color {red} d_2} \\ a_3x + b_3y + c_3z&= {\颜色{红} D_3} \ {结束矩阵} \权。$</big></p><p>以矩阵格式表示</p><p><big></big></p><p><big>$ \ begin {bmatrix} a_1&b_1&c_1 \\ a_2&b_2&c_2 \\ a_3&b_3&c_3 \ end {bmatrix} \ begin {bmatrix} x \\ y \\ z \ end {bmatrix} = \ begin {bmatrix} {\ color {red} d_1} \\ {\ color {red} d_2} \\ {\ color {red} d_3} \ end {bmatrix}。$</big></p><p>然后可以找到$ x,y $和$ z $的值,如下所示: </p><p><big></big></p><p><big>$ x = \ frac {\ begin {vmatrix} {\ color {red} d_1}&b_1&c_1 \\ {\ color {red} d_2}&b_2&c_2 \\ {\ color {red} d_3}&b_3& c_3 \ end {vmatrix}} {\ begin {vmatrix} a_1&b_1&c_1 \\ a_2&b_2&c_2 \\ a_3&b_3&c_3 \ end {vmatrix}},\ quad y = \ frac {\ begin {vmatrix } a_1&{\ color {red} d_1}&c_1 \\ a_2&{\ color {red} d_2}&c_2 \\ a_3&{\ color {red} d_3}&c_3 \ end {vmatrix}} {\ begin {vmatrix} a_1&b_1&c_1 \\ a_2&b_2&c_2 \\ a_3&b_3&c_3 \ end {vmatrix}},\ text {和} z = \ frac {\ begin {vmatrix} a_1&b_1&{\ color {red} d_1} \\ a_2&b_2&{\ color {red} d_2} \\ a_3&b_3&{\ color {red} d_3} \ end {vmatrix}} {\ begin {vmatrix} a_1&b_1& c_1 \\ a_2&b_2&c_2 \\ a_3&b_3&c_3 \ end {vmatrix}}。$</big></p>任务<p>给定以下方程组: </p><p><big>$ \ begin {例} 2w-x + 5y + z = -3 \\ 3w + 2x + 2y-6z = -32 \\ w + 3x + 3y-z = -47 \\ 5w-2x-3y + 3z = 49 \\ \ end {cases} $</big></p><p>使用Cramer的规则解决<big>$ w $,$ x $,$ y $</big>和<big>$ z $</big> 。 </p>