Finding the determinant ( Linear Algebra)

Question

Using elementary row or column operations to find the determinant. 

|3   8  7|

|0  -5  4|

|6   1  6|

Answer 1

The idea is to change the determinant to one which is upper or lower triangular. One you can get it into this form, the determinant is just the product of the three main diagonal entries.

 

Here is a suggestion.

 

Try multiplying row 1 by -2 and adding it to row 3. This will produce a zero in the 3,1 entry.

 

I won't show you what happens after you do this, but the next step will be to get a zero in the third row and second column in the same way using the second row. It can be done, though I won't show you the row operation which is needed.

 

After you do these two row operations, the determinant will have zeros BELOW the main diagonal. You can then multiply those three numbers together to get the determinant of the original matrix. This is because the row operation you are using DOES NOT CHANGE the determinant each time you apply it.

 

The correct answer will be a fairly large (but not too large) number.

 

Let me know if you need more help on this after you have tried it yourself.