Cramer's rule for finding the inverse of an $n times n$ matrix
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Working off of this wikipedia article. I can understand all parts of the proof of cramer's rule, except for why $A_ij = 0$ for all $i neq j$, where $A_ij$ denotates the $i$th row and the $j$th column if the matrix $A$. I was wondering if anyone could explain to me why that must be the case. If this is something which ought to be self-evident please point me towards a video or article which could educate me on the principles I am missing.
EDIT: the part i do not follow is the last sentence of the second paragraph of the proof section of the aforementioned Wikipedia article.
linear-algebra
asked Aug 9 at 15:50
dudester101
61
add a comment |Â
up vote
0
down vote
favorite
Working off of this wikipedia article. I can understand all parts of the proof of cramer's rule, except for why $A_ij = 0$ for all $i neq j$, where $A_ij$ denotates the $i$th row and the $j$th column if the matrix $A$. I was wondering if anyone could explain to me why that must be the case. If this is something which ought to be self-evident please point me towards a video or article which could educate me on the principles I am missing.
EDIT: the part i do not follow is the last sentence of the second paragraph of the proof section of the aforementioned Wikipedia article.
linear-algebra
asked Aug 9 at 15:50
dudester101
61
Can you point to the precise line or sentence where they use the statement which you don't follow? Skimming through the article I wasn't able to find what you're looking for.
– Lukas Miristwhisky
Aug 9 at 16:01
It is because there are two repeated columns.
– user582578
Aug 9 at 16:02
the part i do not follow is the last sentence of the second paragraph of the proof section.
– dudester101
Aug 9 at 21:45
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Working off of this wikipedia article. I can understand all parts of the proof of cramer's rule, except for why $A_ij = 0$ for all $i neq j$, where $A_ij$ denotates the $i$th row and the $j$th column if the matrix $A$. I was wondering if anyone could explain to me why that must be the case. If this is something which ought to be self-evident please point me towards a video or article which could educate me on the principles I am missing.
EDIT: the part i do not follow is the last sentence of the second paragraph of the proof section of the aforementioned Wikipedia article.
linear-algebra
asked Aug 9 at 15:50
dudester101
61
Working off of this wikipedia article. I can understand all parts of the proof of cramer's rule, except for why $A_ij = 0$ for all $i neq j$, where $A_ij$ denotates the $i$th row and the $j$th column if the matrix $A$. I was wondering if anyone could explain to me why that must be the case. If this is something which ought to be self-evident please point me towards a video or article which could educate me on the principles I am missing.
EDIT: the part i do not follow is the last sentence of the second paragraph of the proof section of the aforementioned Wikipedia article.
linear-algebra
asked Aug 9 at 15:50
dudester101
61
edited Aug 9 at 21:44
asked Aug 9 at 15:50
dudester101
61
asked Aug 9 at 15:50
dudester101
61
asked Aug 9 at 15:50
dudester101
61
61
Can you point to the precise line or sentence where they use the statement which you don't follow? Skimming through the article I wasn't able to find what you're looking for.
– Lukas Miristwhisky
Aug 9 at 16:01
It is because there are two repeated columns.
– user582578
Aug 9 at 16:02
the part i do not follow is the last sentence of the second paragraph of the proof section.
– dudester101
Aug 9 at 21:45
add a comment |Â
Can you point to the precise line or sentence where they use the statement which you don't follow? Skimming through the article I wasn't able to find what you're looking for.
– Lukas Miristwhisky
Aug 9 at 16:01
It is because there are two repeated columns.
– user582578
Aug 9 at 16:02
the part i do not follow is the last sentence of the second paragraph of the proof section.
– dudester101
Aug 9 at 21:45
Can you point to the precise line or sentence where they use the statement which you don't follow? Skimming through the article I wasn't able to find what you're looking for.
– Lukas Miristwhisky
Aug 9 at 16:01
Can you point to the precise line or sentence where they use the statement which you don't follow? Skimming through the article I wasn't able to find what you're looking for.
– Lukas Miristwhisky
Aug 9 at 16:01
It is because there are two repeated columns.
– user582578
Aug 9 at 16:02
It is because there are two repeated columns.
– user582578
Aug 9 at 16:02
the part i do not follow is the last sentence of the second paragraph of the proof section.
– dudester101
Aug 9 at 21:45
the part i do not follow is the last sentence of the second paragraph of the proof section.
– dudester101
Aug 9 at 21:45
add a comment |Â
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Can you point to the precise line or sentence where they use the statement which you don't follow? Skimming through the article I wasn't able to find what you're looking for.
– Lukas Miristwhisky
Aug 9 at 16:01
It is because there are two repeated columns.
– user582578
Aug 9 at 16:02
the part i do not follow is the last sentence of the second paragraph of the proof section.
– dudester101
Aug 9 at 21:45