线性代数,题见下图

2026年09月27日 15:21
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网友(1):

(1)|A2,A3,3A1|
=3|A2,A3,A1|
=-3|A1,A3,A2|
=3|A1,A2,A3|
=3*(-5)
=-15

(2)
|A2-3A1,2A1,A3|
=|A2,2A1,A3|
=2|A2,A1,A3|
=-2|A1,A2,A3|
=(-2)*(-5)
=10
(3)
|A1+A2,A2-3A3,2A3-A1|
=|A1+A2,A2-3A3,2A3+A2|
=|A1+A2,A2-3A3,2A3+3A3|
=|A1+A2,A2-3A3,5A3|
=5|A1+A2,A2-3A3,A3|
=5|A1+A2,A2,A3|
=5|A1,A2,A3|
=5(-5)
=-25