Finite Math Examples
[431321434]⎡⎢⎣431321434⎤⎥⎦
Step 1
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|4∣∣∣2134∣∣∣
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|−3∣∣∣3144∣∣∣
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|1∣∣∣3243∣∣∣
Step 1.9
Add the terms together.
4|2134|-3|3144|+1|3243|4∣∣∣2134∣∣∣−3∣∣∣3144∣∣∣+1∣∣∣3243∣∣∣
4|2134|-3|3144|+1|3243|
Step 2
Step 2.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
4(2⋅4-3⋅1)-3|3144|+1|3243|
Step 2.2
Simplify the determinant.
Step 2.2.1
Simplify each term.
Step 2.2.1.1
Multiply 2 by 4.
4(8-3⋅1)-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.
4⋅5-3|3144|+1|3243|
4⋅5-3|3144|+1|3243|
4⋅5-3|3144|+1|3243|
Step 3
Step 3.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
4⋅5-3(3⋅4-4⋅1)+1|3243|
Step 3.2
Simplify the determinant.
Step 3.2.1
Simplify each term.
Step 3.2.1.1
Multiply 3 by 4.
4⋅5-3(12-4⋅1)+1|3243|
Step 3.2.1.2
Multiply -4 by 1.
4⋅5-3(12-4)+1|3243|
4⋅5-3(12-4)+1|3243|
Step 3.2.2
Subtract 4 from 12.
4⋅5-3⋅8+1|3243|
4⋅5-3⋅8+1|3243|
4⋅5-3⋅8+1|3243|
Step 4
Step 4.1
The determinant of a 2×2 matrix can be found using the formula |abcd|=ad-cb.
4⋅5-3⋅8+1(3⋅3-4⋅2)
Step 4.2
Simplify the determinant.
Step 4.2.1
Simplify each term.
Step 4.2.1.1
Multiply 3 by 3.
4⋅5-3⋅8+1(9-4⋅2)
Step 4.2.1.2
Multiply -4 by 2.
4⋅5-3⋅8+1(9-8)
4⋅5-3⋅8+1(9-8)
Step 4.2.2
Subtract 8 from 9.
4⋅5-3⋅8+1⋅1
4⋅5-3⋅8+1⋅1
4⋅5-3⋅8+1⋅1
Step 5
Step 5.1
Simplify each term.
Step 5.1.1
Multiply 4 by 5.
20-3⋅8+1⋅1
Step 5.1.2
Multiply -3 by 8.
20-24+1⋅1
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