Question

请问这道线性代数题目怎么做?

需要详细过程谢谢！

Answer 1

D = 1A11+2A12+3A13+4A14 =
|1 2 3 4|
|1 -1 0 1|
|2 0 2 -1|
|3 1 3 -1|
D =
|-5 0 -3 6|
| 4 0 3 0|
| 2 0 2 -1|
| 3 1 3 -1|
D =
|-5 -3 6|
| 4 3 0|
| 2 2 -1|
D =
| 7 9 0|
| 4 3 0|
| 2 2 -1|
D = (-1)*
| 7 9|
| 4 3|
= -(21-36) = 15
E = 1M11+2M12+3M13+4M14 = 1A11-2A12+3A13-4A14
|1 -2 3 -4|
|1 -1 0 1|
|2 0 2 -1|
|3 1 3 -1|
E =
|7 0 9 -6|
|4 0 3 0|
|2 0 2 -1|
|3 1 3 -1|
E =
|7 9 -6|
|4 3 0|
|2 2 -1|
E =
|-5 -3 0|
| 4 3 0|
| 2 2 -1|
E = (-1)*
|-5 -3|
| 4 3|
= -(-15+12) = 3