1+x2-2x3+T4 4 ④-3① 2x2-2x3+2x4 5x2+5 3 -6.③ 3 3x3+4 §1矩阵的初等变换 §2矩阵的秋 33线性方程组的解 ③+5② x1+x2-2x3+x4 4.① ④-3② 3+x4 本章总结 6.③ (B3) 去③和④的r2的时,碰巧把r3也消去了 +x4 4.① ④-2③ 3+e 0,② 3,③ (B4) 0 第5页共41页 此时④是恒等式,若不是恒等式就说明方程组无解 (B4)是4个未知量3个有效方程的方程组,肯定有个自由未知变量,“回代”的 全屏显示 方法求解:将③x4=-3代入②得x2=3+3,将x4=-3,x2=x3+3代入 ①,得x1=x3+4天津师范大学 §1 Ý ✡ ✛ Ð ✤ ❈ ❺ §2 Ý ✡ ✛ ➑ §3 ❶ ✺ ➄ ➜ ⑤ ✛ ✮ §4 Ð ✤ Ý ✡ ✢Ù♦✭ ❒ù: Ü✟r ■ ❑ ➄ JJ II J I ✶ 5 ➄ ✁ 41 ➄ ❼ ↔ ✜ ➯ ✇ ➠ ✬ ✹ ò Ñ ✗−✘ ✘−2✗ ✙−3✖ −→    x1 + x2 −2 x3 + x4 = 4, ✖ 2 x2 −2 x3 +2 x4 = 0, ✗ −5 x2 +5 x3 −3 x4 = −6, ✘ 3 x2 −3 x3 +4 x4 = −3, ✙ (B2) ✗× 1 2 ✘+5✗ ✙−3✗ −→    x1 + x2 −2 x3 + x4 = 4, ✖ x2 − x3 + x4 = 0, ✗ 2 x4 = −6, ✘ x4 = −3, ✙ (B3) ➒✖✘Ú✙✛x2✛➒,✲⑤rx3➃➒✖✡. ✘↔✙ ✙−2✘ −→    x1 + x2 −2 x3 + x4 = 4, ✖ x2 − x3 + x4 = 0, ✗ x4 = −3, ✘ 0 = 0, ✙ (B4) ❞➒✙➫ð✤➟, ❡Ø➫ð✤➟Ò❵➨➄➜⑤➹✮. (B4)➫4❻➍⑧þ3❻❦✟➄➜✛➄➜⑤, ➆➼❦❻❣❞➍⑧❈þ, “↔➇”✛ ➄④➛✮: ò✘x4 = −3➇❭✗✚x2 = x3 + 3,òx4 = −3, x2 = x3 + 3➇❭ ✖, ✚x1 = x3 + 4