SOLUTION: Evaluate the following determinants. This is a 3x3 matrix. the 3 is outside of the matrix. |-2 -1 0| 3 |-3 5 -2| | 0 8 -1| Thank you.

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Question 381653: Evaluate the following determinants.
This is a 3x3 matrix. the 3 is outside of the matrix.
|-2 -1 0|
3 |-3 5 -2|
| 0 8 -1|
Thank you.
Answer by Jk22(389)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix

If you have the general 3x3 matrix:



the determinant is:

Which further breaks down to:



Note: , and are determinants themselves.
If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver

--------------------------------------------------------------


From the matrix , we can see that , , , , , , , , and

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

Multiply

Combine like terms.


======================================================================


Answer:

So , which means that the determinant of the matrix is -19


The final determinant is 3³*(-19)=the latter, hence : -513.

We can compare to the matrix multiplied by 3 :

Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix

If you have the general 3x3 matrix:



the determinant is:

Which further breaks down to:



Note: , and are determinants themselves.
If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver

--------------------------------------------------------------


From the matrix , we can see that , , , , , , , , and

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

Multiply

Combine like terms.


======================================================================


Answer:

So , which means that the determinant of the matrix is -513
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