X Use Cramer's rule and the calculator provided to find the value of z that satisfies the system of linear equations. -x+y+2z=-2 -3x+y+z=4 4x+y=3 Note that the ALEKS graphing calculator can be used to make computations easier. The determinant of the coefficient matrix is D = N D

Collinear Points and Determinants a If three points lie on a line, what is the area of the triangle that they determine? Use the answer to this question, together with the determinant formula for the area of a triangle, to explain why the points (a1,b1), (a2,b2) and (a3,b3) are collinear if and only if |a1b11a2b21a3b31|=0 b Use a determinant to check whether each set of points is collinear. Graph them to verify your answer. i (6,4), (2,10), (6,13) ii (5,10), (2,6), (15,2)

Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is O. For simplicity, use a 22 .

Find the determinant of the matrix. [4032013501511103]