SOLUTION: Find the value of the determinant | -2 5 4 | | 3 -2 1 | | 1 6 -3 |

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the value of the determinant | -2 5 4 | | 3 -2 1 | | 1 6 -3 |      Log On


   

Question 935786: Find the value of the determinant
| -2 5 4 |
| 3 -2 1 |
| 1 6 -3 |
Answer by MathLover1(20850) 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

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


From the matrix %28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29, we can see that a=-2, b=5, c=4, d=3, e=-2, f=1, g=1, h=6, and i=-3

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29=0--50%2B80 Multiply

abs%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29=130 Combine like terms.


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


Answer:

So abs%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29=130, which means that the determinant of the matrix %28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29 is 130