State whether the following statements are true or false The

State whether the following statements are true or false: The function T : R^2 rightarrow y R^3 given by T(x_1,x_2) = (2x_1 + 3x_2,4x_2 - 1 - x_1,x_1) is a linear transformation.____If T : V rightarrow W be an isomorphism, then ker(T) = {0}.___Every square matrix has a LU-decomposition.____If A is an m times n matrix, then A^TA is an m times m matrix.____In linear programming problems, all variables are restricted to positive values only.___One of the quickest ways to plot a constraint is to find the two points where the constraint crosses the axes, and draw a straight line between these points.____

Solution

(a) True

(b) True

(c) False

(d) True

(e) True

(f) True