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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
Solve the following system of linear equations by using the inverse matrix method X+Y+Z=4 -2X-Y+3Z=1 Y+5Z=9
For the following exercises, solve a system using the inverse of a 3 x 3 matrix. 16.4x + 4y + 4z = 40 4 4 х 140 2x - 3y + 4z = -12 -3 4 y - x + 3y + 4z = 9 -1 3 4 2 -12 2 G
Solve the linear system using an inverse matrix. -4x +5y 12 The inverse of the coefficient matrix A, A 1 is (Simplify your answer. Type an integer or simplified fraction for each matrix element) The solution to the system is x-and y Simplify your answers. Type integers or simplified fractions) Enter your answer in each of the answer boxes
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
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...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9. Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9 Solve the following problem using Lagrange...
5. For the system, 4x + y + 2z = 1 2x + 3y + 4z = -5 x – y +3z = 3 Find the rank of the coefficient matrix by calculating the determinant. Use Cramer's theorem to find the solution of this system. (10 points) 6. Find the inverse of the following matrix using Gauss-Jordan method. Verify your result by computing the inverse using the method of determinants. (10 points) 1 2 4 2 4 2 1] 1...