# Linear Algebra Examples

Step 1
Refer to the corresponding sign matrix below.
Step 2
Use the sign matrix and the given matrix, , to find the cofactor of each element.
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
The cofactor matrix is a matrix with cofactors as the elements.
Step 3
Transpose the cofactor matrix to find the adjoint.
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.