Finite Math Examples

[431321434]431321434
Step 1
Choose the row or column with the most 00 elements. If there are no 00 elements choose any row or column. Multiply every element in row 11 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 a11a11 is the determinant with row 11 and column 11 deleted.
|2134|2134
Step 1.4
Multiply element a11a11 by its cofactor.
4|2134|42134
Step 1.5
The minor for a12a12 is the determinant with row 11 and column 22 deleted.
|3144|3144
Step 1.6
Multiply element a12a12 by its cofactor.
-3|3144|33144
Step 1.7
The minor for a13a13 is the determinant with row 11 and column 33 deleted.
|3243|3243
Step 1.8
Multiply element a13a13 by its cofactor.
1|3243|13243
Step 1.9
Add the terms together.
4|2134|-3|3144|+1|3243|4213433144+13243
4|2134|-3|3144|+1|3243|
Step 2
Evaluate |2134|.
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Step 2.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
4(24-31)-3|3144|+1|3243|
Step 2.2
Simplify the determinant.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Multiply 2 by 4.
4(8-31)-3|3144|+1|3243|
Step 2.2.1.2
Multiply -3 by 1.
4(8-3)-3|3144|+1|3243|
4(8-3)-3|3144|+1|3243|
Step 2.2.2
Subtract 3 from 8.
45-3|3144|+1|3243|
45-3|3144|+1|3243|
45-3|3144|+1|3243|
Step 3
Evaluate |3144|.
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Step 3.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
45-3(34-41)+1|3243|
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 3 by 4.
45-3(12-41)+1|3243|
Step 3.2.1.2
Multiply -4 by 1.
45-3(12-4)+1|3243|
45-3(12-4)+1|3243|
Step 3.2.2
Subtract 4 from 12.
45-38+1|3243|
45-38+1|3243|
45-38+1|3243|
Step 4
Evaluate |3243|.
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Step 4.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
45-38+1(33-42)
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 3 by 3.
45-38+1(9-42)
Step 4.2.1.2
Multiply -4 by 2.
45-38+1(9-8)
45-38+1(9-8)
Step 4.2.2
Subtract 8 from 9.
45-38+11
45-38+11
45-38+11
Step 5
Simplify the determinant.
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Step 5.1
Simplify each term.
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Step 5.1.1
Multiply 4 by 5.
20-38+11
Step 5.1.2
Multiply -3 by 8.
20-24+11
Step 5.1.3
Multiply 1 by 1.
20-24+1
20-24+1
Step 5.2
Subtract 24 from 20.
-4+1
Step 5.3
Add -4 and 1.
-3
-3
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 [x2  12  π  xdx ] 
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