Prove that the following determinant equals 0
$begingroup$
We have a $n*n$ matrix $A=(a_{i,j})$.
If $i=j$, then $a_{i,j}=1-n$. otherwise, $a_{i,j}=1$. Show that $|A|=0$.
I tried using gauss elimination but it just gets too complicated. I also tried to do $R_i rightarrow R_i-R_1/(1-n)$ for all $i>1$, and then expand over the first column, but it also didn't work for me. Can someone please help?
linear-algebra determinant
asked 2 hours ago
OmerOmer
2908
$endgroup$
add a comment |
$begingroup$
We have a $n*n$ matrix $A=(a_{i,j})$.
If $i=j$, then $a_{i,j}=1-n$. otherwise, $a_{i,j}=1$. Show that $|A|=0$.
I tried using gauss elimination but it just gets too complicated. I also tried to do $R_i rightarrow R_i-R_1/(1-n)$ for all $i>1$, and then expand over the first column, but it also didn't work for me. Can someone please help?
linear-algebra determinant
asked 2 hours ago
OmerOmer
2908
$endgroup$
add a comment |
$begingroup$
We have a $n*n$ matrix $A=(a_{i,j})$.
If $i=j$, then $a_{i,j}=1-n$. otherwise, $a_{i,j}=1$. Show that $|A|=0$.
I tried using gauss elimination but it just gets too complicated. I also tried to do $R_i rightarrow R_i-R_1/(1-n)$ for all $i>1$, and then expand over the first column, but it also didn't work for me. Can someone please help?
linear-algebra determinant
asked 2 hours ago
OmerOmer
2908
$endgroup$
We have a $n*n$ matrix $A=(a_{i,j})$.
If $i=j$, then $a_{i,j}=1-n$. otherwise, $a_{i,j}=1$. Show that $|A|=0$.
I tried using gauss elimination but it just gets too complicated. I also tried to do $R_i rightarrow R_i-R_1/(1-n)$ for all $i>1$, and then expand over the first column, but it also didn't work for me. Can someone please help?
linear-algebra determinant
linear-algebra determinant
asked 2 hours ago
OmerOmer
2908
asked 2 hours ago
OmerOmer
2908
asked 2 hours ago
OmerOmer
2908
asked 2 hours ago
OmerOmer
2908
asked 2 hours ago
OmerOmer
2908
2908
add a comment |
add a comment |
1 Answer
1
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$begingroup$
Hint:$$
Aleft(begin{array}{c}1\1\vdots\1end{array}right)=0.
$$
answered 2 hours ago
SongSong
7,991423
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
oldest
votes
active
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$begingroup$
Hint:$$
Aleft(begin{array}{c}1\1\vdots\1end{array}right)=0.
$$
answered 2 hours ago
SongSong
7,991423
$endgroup$
add a comment |
$begingroup$
Hint:$$
Aleft(begin{array}{c}1\1\vdots\1end{array}right)=0.
$$
answered 2 hours ago
SongSong
7,991423
$endgroup$
add a comment |
$begingroup$
Hint:$$
Aleft(begin{array}{c}1\1\vdots\1end{array}right)=0.
$$
answered 2 hours ago
SongSong
7,991423
$endgroup$
Hint:$$
Aleft(begin{array}{c}1\1\vdots\1end{array}right)=0.
$$
answered 2 hours ago
SongSong
7,991423
answered 2 hours ago
SongSong
7,991423
answered 2 hours ago
SongSong
7,991423
answered 2 hours ago
SongSong
7,991423
7,991423
add a comment |
add a comment |
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