Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(A) = det(A) from R5X5 to R B. T(A) = trace(A) from R6x6 to R >= [1 1 ²] ₁ D. T(A) = AT from R3x5 to R5x3 E. T(A) = A7 from R 4x4 to R4x4 to R4x5 F. T(A)= 6A from R 4x5 C.T(A) = A from R2x3 to R2x3

Consider the graph of Ax + By = C where A, B, and C are positive constants and A = B. If the value of B is increased, what happens to the x-intercept? The x-intercept moves away from the origin. The value of the x-intercept changes sign. The x-intercept moves closer to the origin. The x-intercept does not change. The value of the x-intercept becomes 0. O O X

12&13

R 2. Describe a series of transformations that would transform f(x) = |x| + 5 into g(x) = −2|x|- 1 Be sure to clearly communicate your reasoning using mathematical academic vocabulary.