# Linear Algebra Examples

Refer to the corresponding sign matrix below.

The determinant of is .

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Add and .

The determinant of is .

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 .

The determinant of is .

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

The determinant of is .

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 .

The determinant of is .

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Add and .

The determinant of is .

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 .

The determinant of is .

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Add and .

The determinant of is .

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Simplify the expression.

Add and .

Multiply by .

The determinant of is .

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.

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.