Consider a linear transformation T from R to R2 for which T and T Find the matrix A of T. A =

Assume that T is a linear transformation. Find the standard matrix of T. T: R2→R*, T(e,) = (8, 1, 8, 1), and T(e2) = (-6, 9, 0, 0), where e, = (1,0) and e, = (0,1).

Find the matrix A of T. A = Consider a linear transformation T from R³ to R² for which [ T (B)-(B)-(F)-A T T

3. Let T : R² → R² be the linear transformation that rotates each point in R² about the origin through the angle π/4, counterclockwise. Determine the standard matrix for T.

Consider a linear transformation T from R³ to R² for which Find the matrix A of T. +46 A = T (B)-· *(B)-· *(8) - A T T

Find the matrix A of T. A= Consider a linear transformation T from R³ to R² for which = E T = [8]. T = T * (E) - · *(8) - · *(6) - A -H). =

Let T be the linear transformation defined by T(x, y) = (-9y,4x + y, 5y – 8x, 2y – 7x). Find its associated matrix A. A =

Let S be a linear transformation from R2 to R2 with associated matrix 11. Let T be a linear transformation from R2 to R2 with associated matrix -F A = C= B = 2 Determine the matrix C of the composition To S. -3 2] 0 2

Suppose that f : R² → R² is the linear transformation which first rotates a vector 90 degrees clock- wise and then multiplies the first coordinate by 2. Find a 2 × 2 matrix A such that f(x) = Ax for any vector x E R².

Find the matrix A of T. A = Consider a linear transformation T from R³ to R² for which = ¹(E)) - ¤) ¹(C) - ¤) ¹(E)) - Q T = T = · T = " 72