2. a) Find the dimension of the solution space of the homogeneous linear system (1 point)...
=0 1. Find a basis for the solution space of the homogeneous linear system and find its dimension. 2 -34, +13 2x; -6x9 +223 =0 3x; -92, + 3x3 = 0
Find the basis and the dimension of the following linear
solution system:
x + y + z = 0, 3x + 2y – 2z = 0, 4x + 3y – z = 0 and 6x + 5y +z = 0
2. Find the basis for the solution space of the homogeneous system: a. X+2y = 0 2x+4y=0 b. 3x+2y+4z=0 2x+ y - 2 = 0 x +y +3z =0
4. Find a basis for the solution space of the homogeneous linear system (aka find the basis for the null space), and then find the dimension of that space. 21 2+230 2x1+x2 + 3x3 = 0 21-6r2 +230 31-92 +330
21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3 +14 213r2+4r3- 5x4 4x1+6r2 +8T3- 10x4 6r1 +9r2 +12r3 - 15r4= 0 0 Your solution must include verification that the basis spans the set of all solutions and is linearly independent.
21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3 +14 213r2+4r3- 5x4 4x1+6r2 +8T3-...
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
A linear system may have a unique solution, no solution, or infinitely many solutions. Indicate the type of the system for th following examples by U , N , or I7x+3y= pi 4x-6y= pi^2 2x+3y= 0 4x+6y= 0 2x+3y=1 4x+ 6y= 1x+y=5 x+2y=102x-3y=5 4x-6y=10
Use Gaussian elimination to find the complete solution to each system (X-3y + z = 1 -2x + y + 3z =-7 x-4y + 2z = 0 A ((2t + 4, t + 1, t)h 0-B. {(2t + 5, t+2,t)) OC. (1t + 3, t + 2, t) D. ((3t 3, t+ 1, t))
1. Let 1 -1][-1 s={ 112 [1] 1 1 Find a basis for the subspace W = span S of M22. What is the dim W? 2. Find the basis for the solution space of the homogeneous system: a. x+2y = 0 2x+4y =0 b. 3x+2y+4z=0 2x+ y - Z = 0 x +y +3z =0
Solve the following linear programming models graphically and explain the solution results based on the different solution types we discussed in class. a) Formulation 1 Subiect to: AX 12 X,Y 20 b) Formulation 2 Max Z = X + 4Y Subject to: 2X +3Y 3 24 Y 2 1 X,Y 2 0 c) Formulation 3 Subject to: X 2 4 6X 6Y 2 42 Y 2 2
Solve the following linear programming models graphically and explain the solution results based...