01 2 Points True or False? Q1.1 1 Point Every matrix transformation is a linear transformation. That is, if T : R" -> RM is defined by the formula T(x) = Ax for some matrix A, then T is a linear transformation. O True O False Save Answer Q1.2 1 Point Every linear transformation from R" to IR" is a matrix transformation. That is, if T : R" - R' is a linear transformation, then there exists a matrix A such that T(x) = Ax. O True O False Save Answer Q2 2 Points Q2.1 1 Point A= 4 2 -1 01 3 2 The formula T(x) = Ax defines a transformation T : " -> RM. Enter the correct value that should be written in place of m in the previous sentence. Save Answer Q2.2 1 Point T(x) = 0 -1 X Which of the following best describes the transformation T? O T is a projection. O T is a reflection. O T is a rotation. O T is a shearing transformation. Save Answer Q3 4 Points Let T : 4 -> Ry be the linear transformation defined by the formula [x1 + 23 + 2x4] = X2 + 23 + 24 -x1 + 2x2 + 23] i. (2 points) Find the standard matrix of T. ii (2 points) Determine if T' is one-to-one and determine if T' is onto. Please select file(s) Select file(s) Save Answer Q4 4 Points Let A = 5 1 7. Let S : IR3 -> IR2 be the linear transformation whose standard matrix is A. Let U : R2 -> R' be the linear transformation whose standard matrix is A (the transpose of A). Let P : R3 -> RS be the linear transformation which first applies S and then applies U. Let Q : R2 -> R2 be the linear transformation which first applies U and then applies S. Find the standard matrix of P and the standard matrix of Q. Clearly indicate which is which in your work. Please select file(s) Select file(s) Save