b) Consider the system of simultaneous equations for x,y and z: ( x + 2y + z = 3 r-3y+z=1 (2x - y +2 = 4 Use Gaussian elimination to find if these equations are consistent. Pro- vide a geometrie interpretation of the result. (18 marks) [Total 35 marks)
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
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
Systems of Equations: 3x + y = 6 2x-2y=4 Substitution: Elimination: Solve 1 equation for 1 variable. Find opposite coefficients for 1 variable. Rearrange. Multiply equation(s) by constant(s). Plug into 2nd equation Add equations together (lose 1 variable). Solve for the other variable. Solve for variable. Then plug answer back into an original equation to solve for the 2nd variable. y = 6 -- 3x solve 1" equation for y 6x +2y = 12 multiply 1" equation by 2 2x...
ASAP please 1. Solve the following simultaneous equations (1) graphically and (ii) using the elimination method. (a) 2x + 3y = 12.5 -x +2y =6 (y on the vertical axis) (b) 4p - 3Q = 3 P +20 = 20 (p on the vertical axis)
Solve the system of nonlinear equations using substitution or elimination {x^2+y^2=13 (2x-3y=0
20: Solve the system of equations using substitution method. 2x+5y=26 X+ y= 10 21: Solve the following equation. x-x1/2-6= 0 22: Solve the following system of equations, using elimination method. 2x+3y = 5 5x- y = 4 23: Solve the system of nonlinear equations. Any Method. Y?=x2-9 2y= x-3 24: Convert the log into exponent form. Ln (3x-5)2= 16 25: f(x)= 1/x in words explain the transformation of the following functions. a. g(x) = 1/ (x-3) +5 b. h(x)= -1/(x+2)...
Name: Fased Al Hamvn own EE201 Quiz4 Solve the equations: 20p-23 Solutions: xy (2) 4x+3y-11 2x-y 3 Solutions: x= 1 , ys.⑦ x+y=6 7x-y=10 x-3 yー2 +, y,6 Solutions: , x-2y + 3z = 2 0 Solutions: x 2x-y+3z 5 x+3y-2z =-1 (5) Solutions: x- , y= , z=
Problem ONE UseGauss-Jordan method to solve the following system of linear equations 2x - 3y +z = 0 5x + 4y +z = 10 2x - 2y - z= -1 Problem TWO Find the eigenvalues and the corresponding eigenvectors of the matrix [1 0 1 0] 0 1 1 0 0 0 20 LO 0 0 2] Problem THREE Solve the following DE x2y" - 3xy' + 4y = x2 Inx, X>0 Problem FOUR Solve the following DE y (4)...
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or by any convenient method #13 a) 3x+4y-1 2x-3y-12 b) -4x+3y--!5 3x-2y-4