Linear Algebra Examples

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.
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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.
Tap for more steps...
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 cofactor matrix is a matrix with cofactors as the elements.
Transpose the cofactor matrix to find the adjoint.
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Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by moving element in the original matrix to element in the transposed matrix.
Transpose the matrix by turning all rows in original matrix to columns in the transposed matrix.
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