Determimant

MasterPuf

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Hello guys. I am having a problem with the following determinant. http://prntscr.com/dauh23 . My first step is to divide the first column by 2 and then to add it to all the other columns. After that I multiply the number at position aii with -3/aii and then I add that column to the first one. The problem is that I can't determine the number a11 .
 
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Hello guys. I am having a problem with the following determinant. http://prntscr.com/dauh23 . My first step is to divide the first column by 2 and then to add it to all the other columns. After that I multiply the number at position aii with -3/aii and then I add that column to the first one. The problem is that I can't determine the number a11 . T
For other readers, the determinant is as follows:

. . . . .\(\displaystyle \left| \begin{array}{ccccccc} 6&8&8&8&8&...&8 \\ 6&-3\, +\, n.1&-3&-3&-3&...&-3 \\ 6&-3&-3\, +\, 1.2&-3&-3&...&-3 \\ 6&-3&-3&-3\, +\, 2.3&-3&...&-3 \\ 6&-3&-3&-3&3\, +\, 3.4&...&-3 \\ ...&...&...&...&...&...&... \\ 6&-3&-3&-3&-3&...&-3\, +\, (n\, -\, 1).n \end{array} \right|\)

;)
 
Hello guys. I am having a problem with the following determinant. http://prntscr.com/dauh23 . My first step is to divide the first column by 2 and then to add it to all the other columns. After that I multiply the number at position aii with -3/aii and then I add that column to the first one. The problem is that I can't determine the number a11 . T
The line in red above troubles me. How can you just multiply one number in a matrix buy other than 1 and think everything is ok. Also since aii*-3/aii =-3, why not just say that you are simply replacing the entry aii with -3?

Also what is T?
 
The line in red above troubles me. How can you just multiply one number in a matrix buy other than 1 and think everything is ok. Also since aii*-3/aii =-3, why not just say that you are simply replacing the entry aii with -3?

Also what is T?
I am multiplying the first column with 1/2, so I can get a column with 3's . You can't just replace a column with any number, you have to had some operations done on it. That T is just a miss type.
 
Hello guys. I am having a problem with the following determinant. http://prntscr.com/dauh23 . My first step is to divide the first column by 2 and then to add it to all the other columns. After that I multiply the number at position aii with -3/aii and then I add that column to the first one. The problem is that I can't determine the number a11 .

In the given determinant, the first number in the first column is 6. Dividing the first column by 2 (which also divides the value of the determinant by 2) changes that to 3. Is that what you mean by "a11"?

Though, as Jomo said, changing the values of individual numbers in a determinant will change the value of the determinant unpredicatably- it will not help you find the value of the original determinant.

You can use "row" or "column" operations:

If you multiply an entire row or column by a number, that multiplies the determinant by the same number.
If you swap two rows or two columns, that multiplies the determinant by -1.
If you add or subtract a multiple of one row or column to another, that does not change the determinant.
 
In the given determinant, the first number in the first column is 6. Dividing the first column by 2 (which also divides the value of the determinant by 2) changes that to 3. Is that what you mean by "a11"?

Though, as Jomo said, changing the values of individual numbers in a determinant will change the value of the determinant unpredicatably- it will not help you find the value of the original determinant.

You can use "row" or "column" operations:

If you multiply an entire row or column by a number, that multiplies the determinant by the same number.
If you swap two rows or two columns, that multiplies the determinant by -1.
If you add or subtract a multiple of one row or column to another, that does not change the determinant.

I know about the row and column operations. The first thing I do is multiply the determinant and first column by 1/2, then I add the first to all the other columns. So that I can get rid of all the -3's. After that I multiply ''aii'' not ''11'' but ''ii'' meaning the main diagonal. After that I add columns starting from 2 to n to column 1. My question is what do you get as an element for the number at position 1 1, because I can't work out the sequence at 1 1 .
 
I know about the row and column operations. The first thing I do is multiply the determinant and first column by 1/2, then I add the first to all the other columns. So that I can get rid of all the -3's. After that I multiply ''aii'' not ''11'' but ''ii'' meaning the main diagonal. After that I add columns starting from 2 to n to column 1. My question is what do you get as an element for the number at position 1 1, because I can't work out the sequence at 1 1 .
Since the entries in the main diagonal are NOT on any given row and not on any given column you can't multiply the diagonal by any number different by 1 and in the end get the correct value for the original determinant (unless you're amazingly lucky).
 
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