3.7 KiB
title | id | challengeType | videoUrl | localeTitle |
---|---|---|---|---|
Cramer's rule | 59713da0a428c1a62d7db430 | 5 | 克莱默的统治 |
Description
在线性代数中 , Cramer规则是一个线性方程组解的显式公式,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。
特定
$ \ 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。$
以矩阵格式表示
$ \ 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}。$
然后可以找到$ x,y $和$ z $的值,如下所示:
$ 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}}。$
任务给定以下方程组:
$ \ begin {例} 2w-x + 5y + z = -3 \\ 3w + 2x + 2y-6z = -32 \\ w + 3x + 3y-z = -47 \\ 5w-2x-3y + 3z = 49 \\ \ end {cases} $
使用Cramer的规则解决$ w $,$ x $,$ y $和$ z $ 。
Instructions
Tests
tests:
- text: <code>cramersRule</code>是一个函数。
testString: 'assert(typeof cramersRule === "function", "<code>cramersRule</code> is a function.");'
- text: '<code>cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49])</code>应返回<code>[2, -12, -4, 1]</code> 。'
testString: 'assert.deepEqual(cramersRule(matrices[0], freeTerms[0]), answers[0], "<code>cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49])</code> should return <code>[2, -12, -4, 1]</code>.");'
- text: '<code>cramersRule([[3, 1, 1], [2, 2, 5], [1, -3, -4]], [3, -1, 2])</code>应返回<code>[1, 1, -1]</code> 。'
testString: 'assert.deepEqual(cramersRule(matrices[1], freeTerms[1]), answers[1], "<code>cramersRule([[3, 1, 1], [2, 2, 5], [1, -3, -4]], [3, -1, 2])</code> should return <code>[1, 1, -1]</code>.");'
Challenge Seed
function cramersRule (matrix, freeTerms) {
// Good luck!
return true;
}
After Test
console.info('after the test');
Solution
// solution required