Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Then

1) C is empty

2) B has as many elements as C

3) 

4) B has twice as many elements as elements as C  

3. 181 Compute the determinant of the following matrix. You may use any available technique and you may use the properties of determinants to simplify the matrix 4 -13 11 2 2 6 01 A= -10-31 | 4 1 120

3 39. Find the determinant of marks 1 0 -1 37 -2 1 2 -3 0 0 3 1 10 0 4 using elementary row operations to transform the matrix to upper triangular form. Show your work.

2. Find the determinant of N (10 marks]: N [ 1 -2 0 0 0 3 = -2 1 6 -2 4 1 10 2 3 1 0 4 -1 0 4 0 0 -6 -2