Determine whether each statement is true or false If a statement is true give a reason or cite an appropriate statement from the text If a statement is false provide an example that shows the statement is not true in all cases or cite an appropriate statement from the tem a To find the determinant of a triangular matrix add the entries on the main diagonal O True the determinant of a triangular matrix is equal to the order of the matrix which is equal to the sum of the entries in the main diagonal False the determinant of a triangular matrix is equal to the product of the entries in the main diagonal which may not be equal to the sum of the entries in the main diagonal O True the determinant of a triangular matrix is equal to the product of the entries in the main diagonal which is equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the number of nonzero entries in the main diagonal which may not be equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the order of the matrix which may not be equal to the sum of the entries in the main diagonal b To find the determinant of a matrix expand by cofactors in any row or column O False to find the determinant of a matrix expand by cofactors in any row but not in any column O False to find the determinant of a matrix expand by cofactors in only the first column O False to find the determinant of a matrix expand by cofactors in only the first row O True to find the determinant of a matrix expand by cofactors in any row or column False to find the determinant of a matrix expand by cofactors in any column but not in any row X c When expanding by cofactors you need not evaluate the cofactors of zero entries O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be zero True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be one O False in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be zero O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be equal to the cofactor O False in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be equal to the cofactor X