Re: [理工] 99台大資工線代
※ 引述《ste2323 (Endless story)》之銘言：
: http://www.lib.ntu.edu.tw/exam/graduate/99/99406.pdf
: 線代的第二題
: 第一個矩陣是要用行列式的求法嗎？(列運算到上三角?)
: 然後對角線相乘變成純量再乘X向量...好像有點怪怪的
: 剛開始做考古題...被台大砲轟的很慘><
: 請各位大大指點一下
: thx
[2 1 1 1 1 1][x1] [1] [2] [1] [1] [1]
[2 3 2 2 2 2][x2] [2] [2] [3] [2] [2]
[3 3 4 3 3 3][x3] [3] [3] [3] [3] [3]
[4 4 4 5 4 4][x4] = [4] => [4]*x1 + [4]*x2 +...(中略)...+ [4]*x6 = [4]
[5 5 5 5 6 5][x5] [5] [5] [5] [5] [5]
[6 6 6 6 6 7][x6] [6] [6] [6] [7] [6]
因此可得六條聯立方程式如下:
{2*x1 + x2 + x3 + x4 + x5 + x6 = 1
{2*x1 + 3*x2 + 2*x3 + 2*x4 + 2*x5 + 2*x6 = 2
{3*x1 + 3*x2 + 4*x3 + 3*x4 + 3*x5 + 3*x6 = 3
{4*x1 + 4*x2 + 4*x3 + 5*x4 + 4*x5 + 4*x6 = 4
{5*x1 + 5*x2 + 5*x3 + 5*x4 + 6*x5 + 5*x6 = 5
{6*x1 + 6*x2 + 6*x3 + 6*x4 + 6*x5 + 7*x6 = 6
把六條方程式相加：
22*x1 + 22*x2 + 22*x3 + 22*x4 + 22*x5 + 22*x6 = 21
=> 22*(x1+x2+x3+x4+x5+x6) = 21
=> x1+x2+x3+x4+x5+x6 = 21/22
就降@@
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