SOLUTION: Matrix A 5 1 0 -2 3 1 0 2 4 Matrix B -1 2 -3 0 5 4 2 -1 2

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Question 494511: Matrix A
5 1 0
-2 3 1
0 2 4
Matrix B
-1 2 -3
0 5 4
2 -1 2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Matrix A
5 1 0
-2 3 1
0 2 4

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%2C5%2C1%2C0%2C-2%2C3%2C1%2C0%2C2%2C4%29%29, we can see that a=5, b=1, c=0, d=-2, e=3, f=1, g=0, h=2, and i=4

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C5%2C1%2C0%2C-2%2C3%2C1%2C0%2C2%2C4%29%29=50--8%2B0 Multiply

abs%28matrix%283%2C3%2C5%2C1%2C0%2C-2%2C3%2C1%2C0%2C2%2C4%29%29=58 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C5%2C1%2C0%2C-2%2C3%2C1%2C0%2C2%2C4%29%29=58, which means that the determinant of the matrix %28matrix%283%2C3%2C5%2C1%2C0%2C-2%2C3%2C1%2C0%2C2%2C4%29%29 is 58




Matrix B
-1 2 -3
0 5 4
2 -1 2

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-1%2C2%2C-3%2C0%2C5%2C4%2C2%2C-1%2C2%29%29, we can see that a=-1, b=2, c=-3, d=0, e=5, f=4, g=2, h=-1, and i=2

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C-1%2C2%2C-3%2C0%2C5%2C4%2C2%2C-1%2C2%29%29=-14--16%2B30 Multiply

abs%28matrix%283%2C3%2C-1%2C2%2C-3%2C0%2C5%2C4%2C2%2C-1%2C2%29%29=32 Combine like terms.


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


Answer:

So abs%28matrix%283%2C3%2C-1%2C2%2C-3%2C0%2C5%2C4%2C2%2C-1%2C2%29%29=32, which means that the determinant of the matrix %28matrix%283%2C3%2C-1%2C2%2C-3%2C0%2C5%2C4%2C2%2C-1%2C2%29%29 is 32