Let T: R² →R² be a linear transformation that maps u = the fact that T is linear to find the image of 2u + v. A. 8 12 Ов. 2 ○ D. -6 12 - 16 4 -12 5 into and maps v = 5 [:] [10] [2] -2 into 이 -8 Use 4

Which of the following transformations are linear? yi X] + 10 y2 X2 8x1 Yı 7 y2 3x1 + x2 C. -Xi 0. y2 D. 9x2 %3D y2 E.3 y2 Уз 3 X1 7x1 – 2x2 + 6x3 y2 = 10x2 - 3x3 -4x1 – 9x2 F.- Y3 = |L || || || I| || || || IL || || || A. B.

Given the rule (x,y) --> (x-4, y+8), describe what transformation occurs to any given point.

Determine whether the function L: P2 → P2 defined by L(a0 +a1x+a2x2) = a1 +2a2xis a linear transformation. Explain, and show all your work.

Define identity transformation.

Help me solve this linear algebra problem to review for my test.

Let 4-[1] and W-[*] A = w= -[-1³]. Find k so that there exists a vector X whose image under the linear transformation T(x) = Axis w. Note: The image is what comes out of the transformation. k = Find k so that w is a solution of the equation Ax = 0. k =

Need only a handwritten solution only (not a typed one).

Suppose A = -65 -140 30 65 -65 -140 2 a. If possible, complete the following equations; otherwise, enter DNE. -10][3] 30 65 40] f((-10,5)) = f((-10,5)) = and f(x) = Ax. (-10,5) (7,-3) 2 [3] b. The linear transformation facts like multiplication by c. Is the vector (2, -1) an eigenvector for A? choose d. Is the vector (-10, 5) an eigenvector for A? choose e. Are the vectors (2, -1) and (-10, 5) in the same eigenspace? choose f. If the vector (7, k) is an eigenvector for A with eigenvalue -5, then k = in the subspace span{(2, -1)}. If so, what is its associated eigenvalue? If so, what is its associated eigenvalue? g. The linear transformation f acts like multiplication by -5 in the subspace span{ the form . h. Is the vector (-35, 15) an eigenvector for f? choose }. Enter your answer as a coordinate vector of If so, what is its associated eigenvalue?

Find the bilinear transformation whose fixed points are 1,i and maps 0 to -1.