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 1 year 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)= ?

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.

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.

(a) Determine the point of intersection of the line given by (x, y, z) = (4+t, −1+8t, 3+2t), t ∈ R with the plane given by 2x − y + 3z = 15 or show that they do not intersect.

(a) Determine the point of intersection of the line given by (x, y, z) = (4+t, −1+8t, 3+2t), t ∈ R with the plane given by 2x − y + 3z = 15 or show that they do not intersect. (b) Given the line L : X = (9, 13, −3) + t(1, 4, −2), t ∈ R, the point A with position vector 4i+ 16j −3k and that the point P lies on L such that AP is...

Consider the following planes. x + y + z = 7, x + 3y + 3z =...

Consider the following planes. x + y + z = 7, x + 3y + 3z = 7 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = (b) Find the angle between the planes. (Round your answer to one decimal place.) °

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