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I'm an engineer, not a mathematician...
the professor has assigned several proof questions, and I'm having difficulty answering them...
(This may need to be moved to homework help, but the topic is unusual, so I thought I'd get better response here)
Terminology: v is a join operation, ^ is a meet operation D[] is a bracket operation
Example:
Show that when:
[tex] A = a_1 \vee a_2, B = b_1 \vee b_2, \ and\ n = 2 [/tex]
then
[tex] A \wedge B = -D[a_2 , b_1 , b_2] a_1 + D[a_1 , b_1 , b_2] a_2 [/tex]
[tex]= D[a_1 , a_2 , b_2] b_1 - D[a_1 , a_2 , b_1] b_2 [/tex]
If the meet is zero, then assuming that the sets [itex] (a_1, a_2) [/itex] and [itex] (b_1, b_2) [/itex] are both independent, the four brackets must be zero. Show that, in this case, the two subspaces [itex] A_s[/itex] and [itex] B_s [/itex] are the same.
Now, proving the first part is fairly simple: just run though the definition of the meet.
I'm having difficulty with the second part. I thought that the definition of the meet is the intersection of the two subspaces. If the subspaces are the equal, then wouldn't the meet be either As or Bs?
the professor has assigned several proof questions, and I'm having difficulty answering them...
(This may need to be moved to homework help, but the topic is unusual, so I thought I'd get better response here)
Terminology: v is a join operation, ^ is a meet operation D[] is a bracket operation
Example:
Show that when:
[tex] A = a_1 \vee a_2, B = b_1 \vee b_2, \ and\ n = 2 [/tex]
then
[tex] A \wedge B = -D[a_2 , b_1 , b_2] a_1 + D[a_1 , b_1 , b_2] a_2 [/tex]
[tex]= D[a_1 , a_2 , b_2] b_1 - D[a_1 , a_2 , b_1] b_2 [/tex]
If the meet is zero, then assuming that the sets [itex] (a_1, a_2) [/itex] and [itex] (b_1, b_2) [/itex] are both independent, the four brackets must be zero. Show that, in this case, the two subspaces [itex] A_s[/itex] and [itex] B_s [/itex] are the same.
Now, proving the first part is fairly simple: just run though the definition of the meet.
I'm having difficulty with the second part. I thought that the definition of the meet is the intersection of the two subspaces. If the subspaces are the equal, then wouldn't the meet be either As or Bs?
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