Use Cramer's Rule to solve this system for u and u½ and show that the solutions u1 and uz are given by - [ V½f(x) -dx U1 W Yıf (x) -dx W U2 Y1 Y2 ly,' vis the Wronskian. where the determinant W =

Find u x v and show that it is orthogonal to both u and v. u = (-3, 0, 1) v = (8, -2, 0) The cross product of the vectors u = (u1, U2, u3) and v = (V1, V2, V3) is given by a determinant as k u x v = V1 V3

Fill in the blanks with appropriate numbers to calculate the determinant. (a) 9 - • 4 = %3D 1 -1 -3 (b) = ? v1 : O: -3) = 3 -4 1 • 0 - • 2) 3 . -3) • 1 - 2

A: Write the property that makes each of the following determinants-0 Why answer two(1,2,3) 3 1 0 1): 2 3 -2 1 1/3 1 -13 2): 2 0 4-2 1 2 8 Τι π 3): 2 1/2 COS30 3 0 -41 122/7 sin30 √3/2 -Using Grammar's Rule to solve the following system (using determinants) 3x1-2x2 = 4 x1-4x2 = -2 Using the Adjoint of a matrix (adj(A)) to find the inverse A¹ For the following system: 2x + y + z = 3 = x -2z=-7 x-2y+z = −2