1. Find x and z in the following system of equations using Cramer's metho x+y z = 6 3x-2y+z = −5 x + 3y-2z = 14 2. Find the area of triangle with vertices (1, 1), (2, 2), and (5, −1). 3. If A3×3 and B3×3 where det(A) = −2, det(B) = 3, find (a) det(AB-¹) (b) det(A²BT) (c) det(A-¹B³)

If C is the square with vertices (+1, ±1) oriented counter- clockwise, then -y dx + x dy =

Suppose the solution set of a system of linear equations can be described as x₁ = 2-5x4 x₂ = -4x4 x3 = 5 +9x4 with 4 free. a. Write the solution to this system in parametric vector form. x = DNE x+x4

The vector (-1, 1, –3) is a solution of the linear system: X1 + 3x2 – 3x3 = 14 5x1 + 13x2 – 13x3 = 60 -xI - 2x2 + 2x3 = -9 %3D O True O False