2. Find the basis for the solution space of the homogeneous system: a. X+2y = 0...
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
=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
2. a) Find the dimension of the solution space of the homogeneous linear system (1 point) x-3y + z = 0 2x-6y + 2z = 0 2x + 4y-82=0 b) Find a basis for the solution space. (1 point)
Your problem is to find the optimal solution to the following linear programming model where X, Y and Z represent the amounts of products X, Y and Z to produce in order to minimize some cost. Min 4X + 2Y + 6Z s.t. 6X + 7Y + 10Z ≤ 80 (1) 2X + 4Y + 3Z ≤ 35 (2) 4X + 3Y + 4Z ≥ 30 (3) 3X + 2Y + 6Z ≥ 40 (4) X,Y,Z ≥...
12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal. 12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal.
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-...
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
Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x 0, y-t, and Z z(t). If there is no solution, enter NO SOLUTION.) PLEASE 5HOW THE uOK 2x+4y- z=5 x+2y + 4z = 7 (x, y, z) =
Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.) 3y + 2z 4 2x-y-3z 2 2x 2y z6 (x, y, 2) Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.)...
solve the system -x+y+3z=-3 x-2y-2z=8 3x-y-4z=6