Solve the following system of equations and find all congruence class solutions if any exist; if...
Find all solutions to the congruence x2+ x+ 1≡0 mod 91. (Hint:factor the modulus, use trial and error to find the solutions modulo the factors, and the CRT to combine the results into solutions to the original equations.)
Please solve the above 4 questions. 1. Using the extended Euclidean Algorithm, find all solutions of the linear congruence 217x 133 (mod 329), where 0 x < 329 (Eg. if 5n, n 0,. ,6) 24 + 5n, п %3D 0, 1, . .., 6, type 24 + x< 11 2. Find all solutions of the congruence 7x = 5 (mod 11) where 0 (Eg. if 4,7 10, 13, type 4,7,10,13, none. or if there are no solutions, type I 3....
Solve the system of linear equations. Solve the system of linear equations and check any solutions algebraically. parameter a.) x + y + z = 18 2x y + z = 24 3x - Z = 15 (x, y, z) =
(1 point) Find the smallest positive integer solution to the following system of congruence: x = 5 (mod 19) = 2 (mod 5) = 7 (mod 11) x =
Solve the following system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. x + 4y = - 11 5x + 2y = 17 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution of the system is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution is ,y), where...
(3) Solve the following linear congruence: 271 = 12 mod 39. (4) Solve the following set of simultaneous linear congruences: 3x = 6 mod 11, x = 5 mod 7 and 2x = 3 mod 15.
7) Determine if the following congruences have solution(s) and find the solutions if they exist: a. 22x = 4 mob 29 b. 51x = 21 mob 36 C. 35x = 15 mod 182 d. 131x = 21 mob 77 e. 20x = 16 mob 64
Solve for the variable. Identify any extraneous solutions. If no solution exists, explain why. Solve for y: Solve for y: x=y=3 x=> -y+2 y-3
Question 1 : Solve the following system of equations: du at = 22 + +3y dy = 2x + y dt Question 2: State if the following system of equations have Unique solution, no solution or infinite solutions. Explain why? dx = x+2y at dy dt = x+2y
Solve the system of linear equations and check any solutions algebraically. 2x + 4y + z = 3 x – 2y 3z = 4 x + y – z = -1