3. Define a function f : RR by f(x) = mx +b. (a) Show that f...

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3. Define a function f : RR by f(x) = mx +b. (a) Show that f is a linear transformation when b = 0. (b) Find a property of a linear transformations that is violated when b 0. 4. Let TR2 R2 be the linear transformation that first reflects points through the horizontal x1-axis, and then reflects points through the line x1 = x2. (a) Determine the standard matrix for T, whose column vectors are T(e1) and T(e2). (b) Show that T is a rotation about the origin and determine the angle of rotation. 3. Define a function f : RR by f(x) = mx +b. (a) Show that f is a linear transformation when b = 0. (b) Find a property of a linear transformations that is violated when b 0. 4. Let TR2 R2 be the linear transformation that first reflects points through the horizontal x1-axis, and then reflects points through the line x1 = x2. (a) Determine the standard matrix for T, whose column vectors are T(e1) and T(e2). (b) Show that T is a rotation about the origin and determine the angle of rotation.