Let T: R2 + R2 be a linear transformation with PT(x) = 22 – 1. Determine/Compute...
Q8 6 Points Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Decide whether or not such a T is always diagonalizable. Justify your answer.. Q8.2 3 Points Determine/Compute the linear transformation T2 : R2 + R2, VH T(T(u)).
Question Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Determine/Compute the linear transformation T2 : R2 + R?, UH T(T(v)).
(1 point a. The linear transformation T : R2 → R2 is given by: Ti (x, y) = (2x + 9y, 4x + 19y). Find T1x, y). 「-i(x, y) =( x+ y, x+ b. The linear transformation T2 : R' → R' is given by: T2(x, y, z) (x + 2z,2r +y, 2y +z) Find (x, y, z). T2-1(x,y,z)=( x+ y+ z, x+ y+ z, x+ y+ z)
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x) = Ax, where 1 0 2 -1 1 5 1) Find a basis for the kernel of T. 2) Determine the dimension of the kernel of T 3) Find a basis for the image(range) of T. 4) Determine the dimension of the image(range) of T. 5) Determine if it is a surjection or injection or both. 2 6) Determine whether or not v |0|...
(1 point) Let T : P3-> P3 be the linear transformation such that Find T(1). T(x). T(r2), and T(az2 + bz+ c), where a, b, and c are arbitrary real numbers. T(1) = T(z) = T(r2) Note: You can earn partial credit on this problem.
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).
linear algebra Determine whether the function is a linear transformation. T: R2 R3, T(x, y) = (x,xy, vy) O linear transformation O not a linear transformation
(1 point) Let S be a linear transformation from R2 to R2 with associated matrix A= Let T be a linear transformation from IR2 to R2 3 1 ]' Determine the matrix C of the composition ToS
Let t be the linear transformation t: r2 -> r2 that reflects a vector about the line y=x. Find the eigenvalue and eigenvectors of T. How can you interpret this geometrically?
o (translation in R2) Determine whether the function is a linear transformation. T: R2 + R2, T(x, y) = (x + h, y-k), h0 or k linear transformation O not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.)