Which of the following transformations are linear? > 5 || S 5 832 321 > 1...
1 Find the value of h for which the following linear system is consistent and find the general solution in vector form of the resulting consistent linear system. x1+ x2+x3 +2x4 = 3 2x1+2x2+3x3+3x4 = h 5x1+5x2+6x3+9x4 = 10 numbers next to x’s are base numbers
ILUUIPO) Use the simplex method to solve the linear programming problem. Maximize z = 7x1 + 2X2 + X3 subject to: x4 +5x2 + 7x3 58 *4 + 4x2 + 11x3 59 with X, 20, X20, X, 20 O A. Maximum is 9 when xy = 1, X2 = 1, X3 = 0 OB. Maximum is 63 when xy = 9, X2 = 0, X3 = 0 O C. Maximum is 56 when xy = 8, X2 = 0, X3...
Which of the following transformations T R2 → R is linear? A. T(x,y)=5 OB. T(x,y) = x2 OC. None of the given options OD. TIX.Y)=3x+4y OE. T(x,y) = x2 + y2
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)
Solving Systems of Linear Equations Using Linear Transformations In problems 1-5 find a basis for the solution set of the homogeneous linear systems. 2. X1 + x2 + x3 = 0 X1 – X2 – X3 = 0 3. x1 + 3x2 + x3 + x4 = 0 2xı – 2x2 + x3 + 2x4 = 0 x1 – 5x2 + x4 = 0 X1 + 2x2 – 2x3 + x4 = 0 X1 – 2x2 + 2x3 + x4...
please Question 1 Convert the constraints into linear equations by using slack variables. Maximize z = 2X1 +8X2 Subject to:X1 + 6x2 s 15 2x1 + 9x2 s 25 X120,X220 X1 + 6x2 +51 s 15 2X1 + 9x2525 25 x1 +6X2+S1 = 15 2X1 +9x2 +52 = 25 O X1 +6X2 + 512 15 2X1 + 9x2 +522 25 X1 +6x2 = S1 +15 2x1 + 9x2 = S2 + 25 Question 2 Introduce slack variables as necessary and...
B C and E LV VIJ Lou Loui 2. Solve each of the following linear systems using Gaussian Elimination and give a representation of each solution set: a. 2x - y = -3 x+3y = 0 3 - 2y + 2 b. 2x - 4y 2+2 = = = 1 -2 0 4.0 - 2y + 2z c. 2x + 5y + z -2.0 + y - 2 = = = -3 1 2 d 2x1 + 3x2 - 23...
Suppose S CR3 is the intersection of B(0; 2) and the cylinder {(1, y, z) : y2 + 22 <1}, and that 1 the density of S is given by p(x, y, z) = -2 5. Set up an iterated integral which gives the mass of S (you do not need to evaluate it).
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
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 map T R > R< described by reflection in a line L: 2x + 7y = 0 through the origin.