DETERMINANT of matrix $M_n$
$begingroup$
Let $M_n=
begin{bmatrix}
n-1 & n-2 & n-3 & ... & 1& 0\
n-2 & n-3 & n-4 & ... & 0& 1\
n-3 & n-4 & n-5 & ... & 1&2\
vdots & vdots & vdots & ddots & vdots & vdots\
1& 0 & 1 &...& n-3 & n-2\
0 & 1 & 2 &... & n-2&n-1
end{bmatrix}$
What's $det(M_n)$ ?
Can someone help me with this, I tried Using Laplace's formula and transformations of rows but it didn't work.
original problem
linear-algebra
asked Jan 18 at 22:04
m2017mm2017m
94
$endgroup$
add a comment |
$begingroup$
Let $M_n=
begin{bmatrix}
n-1 & n-2 & n-3 & ... & 1& 0\
n-2 & n-3 & n-4 & ... & 0& 1\
n-3 & n-4 & n-5 & ... & 1&2\
vdots & vdots & vdots & ddots & vdots & vdots\
1& 0 & 1 &...& n-3 & n-2\
0 & 1 & 2 &... & n-2&n-1
end{bmatrix}$
What's $det(M_n)$ ?
Can someone help me with this, I tried Using Laplace's formula and transformations of rows but it didn't work.
original problem
linear-algebra
asked Jan 18 at 22:04
m2017mm2017m
94
$endgroup$
1
$begingroup$
Looks like a special case of math.stackexchange.com/questions/770117/….
$endgroup$
– Martin R
Jan 18 at 22:07
1
$begingroup$
@MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1neq a_{11}$. Nevertheless, it may be a OP's typo. We will see...
$endgroup$
– Dog_69
Jan 18 at 22:42
1
$begingroup$
@m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns.
$endgroup$
– Dog_69
Jan 18 at 22:46
1
$begingroup$
there is no typo, formula is good
$endgroup$
– m2017m
Jan 19 at 11:07
add a comment |
$begingroup$
Let $M_n=
begin{bmatrix}
n-1 & n-2 & n-3 & ... & 1& 0\
n-2 & n-3 & n-4 & ... & 0& 1\
n-3 & n-4 & n-5 & ... & 1&2\
vdots & vdots & vdots & ddots & vdots & vdots\
1& 0 & 1 &...& n-3 & n-2\
0 & 1 & 2 &... & n-2&n-1
end{bmatrix}$
What's $det(M_n)$ ?
Can someone help me with this, I tried Using Laplace's formula and transformations of rows but it didn't work.
original problem
linear-algebra
asked Jan 18 at 22:04
m2017mm2017m
94
$endgroup$
Let $M_n=
begin{bmatrix}
n-1 & n-2 & n-3 & ... & 1& 0\
n-2 & n-3 & n-4 & ... & 0& 1\
n-3 & n-4 & n-5 & ... & 1&2\
vdots & vdots & vdots & ddots & vdots & vdots\
1& 0 & 1 &...& n-3 & n-2\
0 & 1 & 2 &... & n-2&n-1
end{bmatrix}$
What's $det(M_n)$ ?
Can someone help me with this, I tried Using Laplace's formula and transformations of rows but it didn't work.
original problem
linear-algebra
linear-algebra
asked Jan 18 at 22:04
m2017mm2017m
94
asked Jan 18 at 22:04
m2017mm2017m
94
edited Jan 19 at 11:05
m2017m
asked Jan 18 at 22:04
m2017mm2017m
94
asked Jan 18 at 22:04
m2017mm2017m
94
asked Jan 18 at 22:04
m2017mm2017m
94
94
1
$begingroup$
Looks like a special case of math.stackexchange.com/questions/770117/….
$endgroup$
– Martin R
Jan 18 at 22:07
1
$begingroup$
@MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1neq a_{11}$. Nevertheless, it may be a OP's typo. We will see...
$endgroup$
– Dog_69
Jan 18 at 22:42
1
$begingroup$
@m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns.
$endgroup$
– Dog_69
Jan 18 at 22:46
1
$begingroup$
there is no typo, formula is good
$endgroup$
– m2017m
Jan 19 at 11:07
add a comment |
1
$begingroup$
Looks like a special case of math.stackexchange.com/questions/770117/….
$endgroup$
– Martin R
Jan 18 at 22:07
1
$begingroup$
@MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1neq a_{11}$. Nevertheless, it may be a OP's typo. We will see...
$endgroup$
– Dog_69
Jan 18 at 22:42
1
$begingroup$
@m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns.
$endgroup$
– Dog_69
Jan 18 at 22:46
1
$begingroup$
there is no typo, formula is good
$endgroup$
– m2017m
Jan 19 at 11:07
1
1
$begingroup$
Looks like a special case of math.stackexchange.com/questions/770117/….
$endgroup$
– Martin R
Jan 18 at 22:07
$begingroup$
Looks like a special case of math.stackexchange.com/questions/770117/….
$endgroup$
– Martin R
Jan 18 at 22:07
1
1
$begingroup$
@MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1neq a_{11}$. Nevertheless, it may be a OP's typo. We will see...
$endgroup$
– Dog_69
Jan 18 at 22:42
$begingroup$
@MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1neq a_{11}$. Nevertheless, it may be a OP's typo. We will see...
$endgroup$
– Dog_69
Jan 18 at 22:42
1
1
$begingroup$
@m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns.
$endgroup$
– Dog_69
Jan 18 at 22:46
$begingroup$
@m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns.
$endgroup$
– Dog_69
Jan 18 at 22:46
1
1
$begingroup$
there is no typo, formula is good
$endgroup$
– m2017m
Jan 19 at 11:07
$begingroup$
there is no typo, formula is good
$endgroup$
– m2017m
Jan 19 at 11:07
add a comment |
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1
$begingroup$
Looks like a special case of math.stackexchange.com/questions/770117/….
$endgroup$
– Martin R
Jan 18 at 22:07
1
$begingroup$
@MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1neq a_{11}$. Nevertheless, it may be a OP's typo. We will see...
$endgroup$
– Dog_69
Jan 18 at 22:42
1
$begingroup$
@m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns.
$endgroup$
– Dog_69
Jan 18 at 22:46
1
$begingroup$
there is no typo, formula is good
$endgroup$
– m2017m
Jan 19 at 11:07