SOLUTION: help me please. what is the value of the determinant? (3x3) |3 6 8| |2 4 0| |3 6 8|

Algebra ->  Matrices-and-determiminant -> SOLUTION: help me please. what is the value of the determinant? (3x3) |3 6 8| |2 4 0| |3 6 8|      Log On


   

Question 207871: help me please. what is the value of the determinant? (3x3)
|3 6 8|
|2 4 0|
|3 6 8|
Found 2 solutions by jim_thompson5910, pjalgeb:
Answer by jim_thompson5910(35256) About Me  (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:

%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29

the determinant is:

Which further breaks down to:



Note: abs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29, abs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29 and abs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29 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 %28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29, we can see that a=3, b=6, c=8, d=2, e=4, f=0, g=3, h=6, and i=8

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29=96-96%2B0 Multiply

abs%28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29=0 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29=0, which means that the determinant of the matrix %28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29 is 0

Answer by pjalgeb(9) About Me  (Show Source):
You can put this solution on YOUR website!
Determinant = (96+0+96) - (96+96+0)
Determinant = 0

Since D = 0 then this system cannot be solved using Determinants.