Solve by using Cramer’s Rule
4 e x – 6 tan( y ) + 2 ln(z) = 1
3 e x + 5 tan( y ) – 3 ln(z) = 2
e x + 5 tan( y ) + 4 ln(z) = 5


Solve using both Gaussian Elimination (row operations) and also Cramer’s Rule x + 3y - 6z = 7 2x - y + 2z = 0 x + y + 2z = -1
Solve the following using Optimization 1) Using substitution: U = 2 ln(x) + ln(y) s.t. 2x + y = 20 2) Using LaGrangian: U = √x + ln(y) s.t. x+y=10 3) Using both: U = 5 ln(x) + 3 ln(y) s.t. 4x + 3y = 100
4. Solve the following system of linear equations using the inverse matrix method. 1 y = 1 2 , 3 2 -r- 1 5 4 a) x+y +z= 6 x-y-3z=-8 x+y- 2z=-6 b) Solve the following system of linear equations using Cramer's Rule. 5. 2 1 -X- 3 2 1 3 X+-y-1 5 4 y = 1 a) x+y+z= 6 x-y-3z=-8 x+y- 2z = -6 b)
4. Solve the following system of linear equations using the inverse matrix method. 1...
Use the Cramer's Rule to solve the system\(2 x-y+z=0\)\(x+y-z=6\)\(4 x-5 y+3 z=28\)Any other method will not be graded ! Justify your answer!
Differential Equations - Seperable equations
(a) y=tan(ln(x)--) 5) 5 (b) y=(31 es2 ds + 27 3
(a) y=tan(ln(x)--) 5)
5 (b) y=(31 es2 ds + 27 3
5. Find the derivative of f(x) = ln (sec(x) + tan *' (x)). 6. Find an equation of the tangent line to the curve y = x’ In(x) when x = e?
Change the system of equations to an augmented matrix. Then Use the Cramer’s Method to solve the system. (1/2)x + (1/5)y = 7 (1/6)x - (2/5)y = -4
Solve using Cramer's Rule X – 2y +z=7 2x +y – z=0 3x + 2y – 2z = -2 O (1,-2,0) O (2,-1,3) O (1,-1,1) No Solution
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
4. Use Inverse method to solve the system and verify your result using Cramer's rule. 2x-y+3z = 9, x+y+z=6,x-y+z=2. [15 Marks 5. Show that the equations X1 + X2 + x,-6, x1 + 2x2 + 3x3 = 14, x1 + 4x2 + 7x3-30 are [10 Marks] consistent and solve them.