(10 pts) Which of the following transformations are linear? y,-9x1 ?

(10 pts) Which of the following transformations are linear? y,-9x1 ?. E. y,-4x2 ?,--3x1
(10 pts) If T : R3 → R3 is a linear transformation such that 2 0 4 0) 4 0 4 and T | |= 0 5 then T
(10 pts) If T : R2 → R2 is a linear transformation such that 0 5 -9 and T 0 -2 2 then the standard matrix of T is A-
(10 pts) Match each linear transformation with its matrix 1. 01 10 2. 10 3. -10 0 1 4. 20 02 5. -10
5. 0 1 -10 6. -1 0 0 -1 A. Reflection in the y-axis B. Reflection in the origin C. Rotation through an angle of 90° in the clockwise direction D. Projection onto the r-axis E. Reflection in the line yx F Dilation by a factor of 2

(10 pts) Find the matrix A of the linear transformation from IR2 to IR3 given by 9 T1 -2 2 T2 -2 -1
(10 pts) -4 -41 24 -1 2 -3 A linear transformation T : R2Ris defined by T(x) - Ar. Find an, in R2 whose image under T is b. r2
(10 pts) Find the matrix A of the linear transformation T from IR2 to R2 that rotates any vector through an angle of 60° in the clockwise direction. [NOTE: if you answer use cos(...) and sin(.), webwork expects the arguments to be in RADIANS.]

(10 pts) Let L be the line in IR3 that consists of all scalar multiples of the vector 2 -2 Find the orthogonal projection of the vector 5 6 onto L