SOLUTION: Can you help me with this one? Show that in any 3x3 determinant if one row is 0, the value of the determinant is 0.

Question 888768: Can you help me with this one?
Show that in any 3x3 determinant if one row is 0, the value of the determinant is 0.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
0,0,0
1,2,3
4,5,6

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

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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.

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Answer:

So , which means that the determinant of the matrix is 0

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