document.write( "Question 494511: Matrix A
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Algebra.Com's Answer #335674 by MathLover1(20850) $\"\"$ $\"About$

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Matrix A \r
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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

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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 $\"%28matrix%283%2C3%2C-1%2C2%2C-3%2C0%2C5%2C4%2C2%2C-1%2C2%29%29\"$ , 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.

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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

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