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- What is a path on the Topologist's comb between (0,1) and (1,0)? Note that the Topologist's Comb is not the same as the Topologist's Wave.Consider two points (x0, y0) and (x1, y1). Prove that the first order Langrange polynonial is equivalent to linear interpolation.What is the sequence of transformation that maps PQR onto P’Q’R’?
- DEFINE: What makes a transformationT : R^n -----> R^m linear?2. Draw the domain of P in the xy-plane. 3. Describe each boundary in terms of only one variable, and give the corresponding range of that variable, for instance “(x,x2) for x ∈ [1,2]”. There can be different choices.Which of the following prescriptions does not define a linear mapping A: R^2 ---> R^2?