问两道线性代数题证明1)|b1+c1 b2+c2 b3+c3| |a1 a2 a3||c1+a1 c2+a2 c3+a3| = 2 |b1 b2 b3||a1+b1 a2+b2 a3+b3| |c1 c2 c3|2)a^2 bc a^2 ac bc abb^2 b^2 ac = bc ab acab c^2 c^2 ab ac bc
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 04:28:51
![问两道线性代数题证明1)|b1+c1 b2+c2 b3+c3| |a1 a2 a3||c1+a1 c2+a2 c3+a3| = 2 |b1 b2 b3||a1+b1 a2+b2 a3+b3| |c1 c2 c3|2)a^2 bc a^2 ac bc abb^2 b^2 ac = bc ab acab c^2 c^2 ab ac bc](/uploads/image/z/10038914-26-4.jpg?t=%E9%97%AE%E4%B8%A4%E9%81%93%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E9%A2%98%E8%AF%81%E6%98%8E1%29%7Cb1%2Bc1+b2%2Bc2+b3%2Bc3%7C+%7Ca1+a2+a3%7C%7Cc1%2Ba1+c2%2Ba2+c3%2Ba3%7C+%3D+2+%7Cb1+b2+b3%7C%7Ca1%2Bb1+a2%2Bb2+a3%2Bb3%7C+%7Cc1+c2+c3%7C2%29a%5E2+bc+a%5E2+ac+bc+abb%5E2+b%5E2+ac+%3D+bc+ab+acab+c%5E2+c%5E2+ab+ac+bc)
问两道线性代数题证明1)|b1+c1 b2+c2 b3+c3| |a1 a2 a3||c1+a1 c2+a2 c3+a3| = 2 |b1 b2 b3||a1+b1 a2+b2 a3+b3| |c1 c2 c3|2)a^2 bc a^2 ac bc abb^2 b^2 ac = bc ab acab c^2 c^2 ab ac bc
问两道线性代数题
证明
1)
|b1+c1 b2+c2 b3+c3| |a1 a2 a3|
|c1+a1 c2+a2 c3+a3| = 2 |b1 b2 b3|
|a1+b1 a2+b2 a3+b3| |c1 c2 c3|
2)
a^2 bc a^2 ac bc ab
b^2 b^2 ac = bc ab ac
ab c^2 c^2 ab ac bc
问两道线性代数题证明1)|b1+c1 b2+c2 b3+c3| |a1 a2 a3||c1+a1 c2+a2 c3+a3| = 2 |b1 b2 b3||a1+b1 a2+b2 a3+b3| |c1 c2 c3|2)a^2 bc a^2 ac bc abb^2 b^2 ac = bc ab acab c^2 c^2 ab ac bc
把第2行的-1倍,第3行的-1倍加到第1行:
b1+c1 b2+c2 b3+c3| |-2a1 -2a2 -2a3|
|c1+a1 c2+a2 c3+a3| = |c1+a1 c2+a2 c3+a3|
|a1+b1 a2+b2 a3+b3| |a1+b1 a2+b2 a3+b3|
把第1行的1/2倍加到第2, 3行:
b1+c1 b2+c2 b3+c3| |-2a1 -2a2 -2a3| |-2a1 -2a2 -2a3|
|c1+a1 c2+a2 c3+a3| = |c1+a1 c2+a2 c3+a3| = |c1 c2 c3 |
|a1+b1 a2+b2 a3+b3| |a1+b1 a2+b2 a3+b3| |b1 b2 b3 |
把第1行的-2提出,并把第2,3行交换得:
|b1+c1 b2+c2 b3+c3| |a1 a2 a3|
|c1+a1 c2+a2 c3+a3| = 2 |b1 b2 b3|
|a1+b1 a2+b2 a3+b3| |c1 c2 c3|