Quandaries and Queries
 

 

I have to find the determinant of the following matrix

 

-2 3 1 2 4
-3 0 -2 5 1
4 2 1 -3 5
2 3 4 -1 2
6 0 3 2 -4
 

 

Hi,

(I am displaying the matrix as a table since it's easier for me to do that.)

When I looked at this matrix I decided to work with the second column since it contains two zeros. I performed three operations

  1. Multiply the first row by -1 and add it to the fourth row.
  2. Multiply the third row by -1 and add it to the first row.
  3. Multiply the first row by -2 and add it to the third row.

This gave me

-6 1 0 5 -1
-3 0 -2 5 1
16 0 1 -13 7
4 0 3 -3 -2
6 0 3 2 -4

which is -1 times

-3 -2 5 1
16 1 -13 7
4 3 -3 -2
6 3 2 -4

Here again I decided to work with the second column. I performed the three operations

  1. Multiply the second row by 2 and add it to the first row.
  2. Multiply the third row by -1 and add it to the fourth row.
  3. Multiply the second row by -3 and add it to the third row.

This gave me

29 0 -21 15
16 1 -13 7
-44 0 36 -23
2 0 5 -2

Thus I have -1 times

29 -21 15
-44 36 -23
2 5 -2

Looking at the third row I decided to add the first column to the third column to get

29 -21 44
-44 36 -67
2 5 0

At this point I decided to expand along the third row and I finally got the value of the determinant to be 319.

Cheers,
Penny

 

 

 
 

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