Define T : R3 → R2 by T(x,y,z) = (2x +4y +3z,6x)
Show that T is linear.
Let T: R3 → R2 T(x, y, z) = (x + y,y+z) a. Is T a linear transformation? b. Find the matrix A of T C. Find the dimension of NUT and image T
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin 8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
Solve the system of linear equations and check any solutions algebraically. 2x + 4y + z = 3 x – 2y 3z = 4 x + y – z = -1
1. Consider the transformation given by T(x, y, z)- (2z 3z+) (a) Show that T is a linear transformation (b) Find the domain and range of T (c) Find the number of columns and r for T. (d) Find the standard matrix for T.
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.
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.
Problem 4. Find basis and dimension of ker and im y for 9: R3 → R2 4(x, y, z) = (2x + y − 32, x + 4y + 2z)
Let Ě =< 2x + 2,3y+z, 6x + 6y > be a vector field in R3. Evaluate the following surface integral directly: xdA || i-dš= $ 8. (XFL) S Where S is the part of the plane 2x + 3y + z = 6 in the first octant (with upward orientation). SHOW ALL OF YOUR WORK!
8) Show that the graph of +692 +9z²&exy 6x z-12yz-2x - 4y +6z+1=0 is degenerate quadric whizh consists plare. nuestion.