Lesson: Properties of Determinants Mathematics

Students will be able to

• understand that the determinant of a matrix remains the same under transposition,
• understand that the determinant equals zero if a matrix includes a row (or column) of elements that are all equal to zero,
• understand that the determinant equals zero if a matrix has a repeated row (or column),
• understand that a common factor in the elements of any row (or column) in a matrix can be factored out of its determinant,
• understand that interchanging any two rows (or columns) of a matrix changes the sign of the determinant,
• understand the sum property of the determinants, which states that if all the elements of any row (or column) are written as a sum of two elements, then the value of the determinant can be expressed as a sum of two determinants,
• understands the invariance property of determinants, which states that the determinant of a matrix remains the same under the operation ,
• understand that multiplying the elements of any row (or column) of a matrix by the cofactors of the corresponding elements in another row (or column) will equal zero,
• understand that the determinant of an upper or lower triangular matrix is the product of the diagonal entries,
• understand that the determinant of a diagonal matrix is the product of the diagonal entries,
• determine the value of an unknown element or unknown variable in a matrix using the properties of determinants.