![Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y, 0 h R R x > sin x g R2R [x, y] [y- x, 2 the m](http://img.homeworklib.com/questions/b20ae4b0-b04a-11eb-b617-f9cbfb7733b1.png?x-oss-process=image/resize,w_560)
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Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y,...
Solve the linear programming problem by simplex method. . Minimize C= -x - 2y + z....
Solve the linear programming problem by simplex method. . Minimize C= -x - 2y + z. subject to 2x + y +2 < 14 4x + 2y + 3z < 28 2x + 5y + 5z < 30 x = 0, y>02 > 0
Algebra Consider the following subsets of R2: C1 = {(2, ) ER: x + 2y <...
Algebra Consider the following subsets of R2: C1 = {(2, ) ER: x + 2y < 4, x > 0,y 0} C2 = {(x,y) € R2 : 2x + y < 4, x > 0, y 20} Draw a sketch of the intersection CinC, and the union CUC2. State whether each set is convex or not. If the set is not convex, give an example of a line segment for which the definition of convexity breaks down.
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2]...
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
#1: Use a change of variables to integrate f (x, y) = y - x over...
#1: Use a change of variables to integrate f (x, y) = y - x over the region described by: –3 <y – 2x < 0 and 0 < 2y – x < 3.
Determine whether the following transformations are linear. A) T(x, y) = (3x, y, y ? x)...
Determine whether the following transformations are linear. A) T(x, y) = (3x, y, y ? x) of R2 ? R3 B) T(x, y) = (x + y, 2y + 5) of R2 ? R2
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x,...
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x, y, z) = (–2x + 2y +z, -x +2y). Find the matrix that corresponds to f with respect to the canonical bases of R3 and R2.
2. Consider the linear functions f: R3 → R2, 9: R3 R3, h: R2 + R...
2. Consider the linear functions f: R3 → R2, 9: R3 R3, h: R2 + R and i: R3 → R4 given by: [ 5x – 72 1 * +54 +92 [2x + 3y +z] y = 3 +9y + 7z IL -+2y 2. + 2y + i i = y +22 |2y – z] (14 (a) Write them as matrices. (b) Which are the compositions we can do using two different functions from above? Do them using matrix multiplication.
Question 3 Solve the following linear program: Max 3x+2y s.t. 2x+2y <8 A 3x+2y < 12...
Question 3 Solve the following linear program: Max 3x+2y s.t. 2x+2y <8 A 3x+2y < 12 B 1x+0.5y < 3C x,y> 0 w How much slack is in constraint B? 2 units of slack O 10 units of slack O 2 units of surplus 10 units of surplus
6. Plot the 3D surface and contour levels of the following function: z(x, y)cos(2y-x) sin(2x) such...
6. Plot the 3D surface and contour levels of the following function: z(x, y)cos(2y-x) sin(2x) such that-π x π and-r y < π [10 marks] 7. Create a 5 x 5 random matrix M6 with elements ranging from 10 to 33. Using indexing, define the following arrays: An array containing all elements of M6 that are greater than 3 and smaller 6 marks] An array containing all elements of M6 that are negative or between 29 and 33. 6 marks...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
Solve the linear programming problem by simplex method. . Minimize C= -x - 2y + z. subject to 2x + y +2 < 14 4x + 2y + 3z < 28 2x + 5y + 5z < 30 x = 0, y>02 > 0
Algebra Consider the following subsets of R2: C1 = {(2, ) ER: x + 2y < 4, x > 0,y 0} C2 = {(x,y) € R2 : 2x + y < 4, x > 0, y 20} Draw a sketch of the intersection CinC, and the union CUC2. State whether each set is convex or not. If the set is not convex, give an example of a line segment for which the definition of convexity breaks down.
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
#1: Use a change of variables to integrate f (x, y) = y - x over the region described by: –3 <y – 2x < 0 and 0 < 2y – x < 3.
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x, y, z) = (–2x + 2y +z, -x +2y). Find the matrix that corresponds to f with respect to the canonical bases of R3 and R2.
2. Consider the linear functions f: R3 → R2, 9: R3 R3, h: R2 + R and i: R3 → R4 given by: [ 5x – 72 1 * +54 +92 [2x + 3y +z] y = 3 +9y + 7z IL -+2y 2. + 2y + i i = y +22 |2y – z] (14 (a) Write them as matrices. (b) Which are the compositions we can do using two different functions from above? Do them using matrix multiplication.
Question 3 Solve the following linear program: Max 3x+2y s.t. 2x+2y <8 A 3x+2y < 12 B 1x+0.5y < 3C x,y> 0 w How much slack is in constraint B? 2 units of slack O 10 units of slack O 2 units of surplus 10 units of surplus
6. Plot the 3D surface and contour levels of the following function: z(x, y)cos(2y-x) sin(2x) such that-π x π and-r y < π [10 marks] 7. Create a 5 x 5 random matrix M6 with elements ranging from 10 to 33. Using indexing, define the following arrays: An array containing all elements of M6 that are greater than 3 and smaller 6 marks] An array containing all elements of M6 that are negative or between 29 and 33. 6 marks...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
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