Linear Algebra Examples

Find the Cofactor Matrix
Refer to the corresponding sign matrix below.
Use the sign matrix and the given matrix, , to find the cofactor of each element.
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The determinant of is .
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by to get .
Multiply by to get .
Subtract from to get .
The determinant of is .
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by to get .
Multiply by to get .
Simplify the expression.
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Subtract from to get .
Multiply by to get .
The determinant of is .
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Subtract from to get .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Simplify the expression.
Tap for more steps...
Subtract from to get .
Multiply by to get .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Subtract from to get .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Simplify the expression.
Tap for more steps...
Subtract from to get .
Multiply by to get .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Subtract from to get .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Simplify the expression.
Tap for more steps...
Subtract from to get .
Multiply by to get .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Subtract from to get .
The cofactor matrix is a matrix with cofactors as the elements.
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