Finite Math Examples

[301244443]
Step 1
Choose the row or column with the most 0 elements. If there are no 0 elements choose any row or column. Multiply every element in row 1 by its cofactor and add.
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Step 1.1
Consider the corresponding sign chart.
|+-+-+-+-+|
Step 1.2
The cofactor is the minor with the sign changed if the indices match a - position on the sign chart.
Step 1.3
The minor for a11 is the determinant with row 1 and column 1 deleted.
|4443|
Step 1.4
Multiply element a11 by its cofactor.
3|4443|
Step 1.5
The minor for a12 is the determinant with row 1 and column 2 deleted.
|2443|
Step 1.6
Multiply element a12 by its cofactor.
0|2443|
Step 1.7
The minor for a13 is the determinant with row 1 and column 3 deleted.
|2444|
Step 1.8
Multiply element a13 by its cofactor.
1|2444|
Step 1.9
Add the terms together.
3|4443|+0|2443|+1|2444|
3|4443|+0|2443|+1|2444|
Step 2
Multiply 0 by |2443|.
3|4443|+0+1|2444|
Step 3
Evaluate |4443|.
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Step 3.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
3(43-44)+0+1|2444|
Step 3.2
Simplify the determinant.
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Step 3.2.1
Simplify each term.
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Step 3.2.1.1
Multiply 4 by 3.
3(12-44)+0+1|2444|
Step 3.2.1.2
Multiply -4 by 4.
3(12-16)+0+1|2444|
3(12-16)+0+1|2444|
Step 3.2.2
Subtract 16 from 12.
3-4+0+1|2444|
3-4+0+1|2444|
3-4+0+1|2444|
Step 4
Evaluate |2444|.
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Step 4.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
3-4+0+1(24-44)
Step 4.2
Simplify the determinant.
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Step 4.2.1
Simplify each term.
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Step 4.2.1.1
Multiply 2 by 4.
3-4+0+1(8-44)
Step 4.2.1.2
Multiply -4 by 4.
3-4+0+1(8-16)
3-4+0+1(8-16)
Step 4.2.2
Subtract 16 from 8.
3-4+0+1-8
3-4+0+1-8
3-4+0+1-8
Step 5
Simplify the determinant.
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Step 5.1
Simplify each term.
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Step 5.1.1
Multiply 3 by -4.
-12+0+1-8
Step 5.1.2
Multiply -8 by 1.
-12+0-8
-12+0-8
Step 5.2
Add -12 and 0.
-12-8
Step 5.3
Subtract 8 from -12.
-20
-20
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 [x2  12  π  xdx ] 
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