T:R ->R3 T(x, y, z) = (2x + 5y − 3z, 4x + y − 5z,...

T:R ->R3 T(x, y, z) = (2x + 5y − 3z, 4x + y − 5z, x − 2y − z) (a) Find the matrix representing this transformation with respect to the standard basis. (b) Find the kernel of T, and a basis for it. (c) Find the range of T, and a basis for it.

Expert Solution

Colby Messinger answered 2 years ago

Solve: 4x - 3z = 1 -3x - z = -3 2x + y + z...

Solve: 4x - 3z = 1 -3x - z = -3 2x + y + z = -1

Maximize p = 2x + 7y + 5z subject to x + y + z ≤...

Maximize p = 2x + 7y + 5z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. P= ? (x, y, z)= ?

Consider a transformation ?:ℝ3→ℝ3T:R3→R3 defined by ?(?,?,?)=(?+?+?, 2?+?, ?−2?+?).T(x,y,z)=(x+y+z, 2x+y, x−2y+z). (a) Find the standard matrix...

Consider a transformation ?:ℝ3→ℝ3T:R3→R3 defined by ?(?,?,?)=(?+?+?, 2?+?, ?−2?+?).T(x,y,z)=(x+y+z, 2x+y, x−2y+z). (a) Find the standard matrix of ?T. (b) Is ?T a linear transformation? Explain. (c) Is ?T invertible? (d) Find the image of (2,−1,1)(2,−1,1) under ?T.

Maximizar P=2x+3y+5z Sujeto a: x+2y+3z ≤ 12 x-3y+2z ≤ 10 x ≥ 0, y...

Maximizar P=2x+3y+5z Sujeto a: x+2y+3z ≤ 12 x-3y+2z ≤ 10 x ≥ 0, y ≥ 0, z ≥ 0 Maximize P=2x+3y+5z Subject to: x+2y+3z ≤ 12 x-3y+2z ≤ 10 x ≥ 0, y ≥ 0, z ≥ 0

W + 2X <----> 5Y + 3Z 0.40 moles of W and 0.40 moles of X...

W + 2X <----> 5Y + 3Z 0.40 moles of W and 0.40 moles of X are placed into a 2.0 liter flask. At equilibrium, 0.70 moles of Y are present in the flask. Calculate the concentration of each specie at equilibrium and calculate the value of equilibrium constant.

solve by determinants a.x+y+z=0 3x-y+2z=-1 2x+3y+3z=-5 b. x+2z=1 2x-3y=3 y+z=1 c. x+y+z=10 3x-y=0 3y-2z=-3 d. -8x+5z=-19...

solve by determinants a.x+y+z=0 3x-y+2z=-1 2x+3y+3z=-5 b. x+2z=1 2x-3y=3 y+z=1 c. x+y+z=10 3x-y=0 3y-2z=-3 d. -8x+5z=-19 -7x+5y=4 -2y+3z=3 e. -x+2y+z-5=0 3x-y-z+7=0 -2x+4y+2z-10=0 f. 1/x+1/y+1/z=12 4/x-3/y=0 2/y-1/z=3

Solve for x,y,z using the inverse if possible. x+2y+5z=2 2x+3y+8z=3 -x+y+2z=3

Given two planes 3x − 2y + z = 1 and 2x + y − 3z...

Given two planes 3x − 2y + z = 1 and 2x + y − 3z = 3. (a). Find the equation for the line that is the intersection of the two planes. (b). Find the equation for the plane that is perpendicular to the two planes.

Given two planes 3x − 2y + z = 1 and 2x + y − 3z = 3.