Determine that the given function is a linear transformation. Prove it (or find its standard matrix) or give a counterexample. Ꮖ xy T x- = T Ꮖ = x + 2y •T([;)])-[27] \([;)])-[**] \([;)])-- = x +
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- Discuss the behavior of(1 point) Find the inverse of the linear transformation Yi 4x1 -1x2 %3D y2 -11x1 +3x2 %D X1 = y2, X2 = Yı+ Y2 - Il||Each one of the lines (a), (b), (c) and (d) represents the linearization of a function at the given point. Some functions ( (i), (ii), and (iii) ) are given below. Work out their linearization and match the linearization with the function. (a) L(x) = -x +1 (b) L(x) (C) L(x) = :-x +1 (d) L(x) = x +1 Here are the functions to be matched: (ii) g(x) = ln(x +2) at a = –1 Choose... + (i) f(x) = e-* at a = 0 Choose... + (iii) h(x) = V1– x at a = 0 Choose... +
- Suppose you know that f : R^2 ---> R^3 is a linear function and that (see picture for given info...). What is f ([3 ,12])? What is f([1,3])? Please note that the matrices I gave are in one column in each of the questions asked.Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are therefrom A to B? Hint: Count the number of m × n matrices with (0,1)-entries.If R is a relation from A to B we define the inverse relation R^-1 from B to A by bR^-1a whenever aRb.If ()=V2- and 9()=1-1 then find the domain of A(x)= f(x)÷g(=) then find the domain of ()= f(r)÷g(r) and OA (-00,1)U(-1,2] OB. (-00,1)U(1,2] Oc (-00,2)(1,2] OD. (-00,-1)U(4,2] O E. (-0,-2)U(1,2] OC.
- Determine whether each of these functions is a bijection from R to R. f(x) = x^2 + 1 f(x) =(x^2 +1)/(x^2 + 2) f(x) =IxI f(x) =x/2Determine whether the following sets are linearly dependent or linearlyindependent. (a) {(; )( )} . -9} in Maxa(R) 4 (b) {(- ).(- 9G -)} in M2x2(R) 4 (c) {x 3 + 2x2, -x2 + 3x + 1, x3 – x2 + 2x – 1} in P3(R) (d) {x 3 – x, 2x2 + 4, -2x3 + 3x2 + 2x + 6} in P3(R) (e) {(1, -1, 2), (1, -2, 1), (1, 1, 4)} in R3 (f) {(1, –1, 2), (2, 0, 1), (–1, 2, –1)} in R3 {(÷ ) ( -) (; 0. 2 ).(- )} in Max2(R) (g) (m) {(-; ') (? ). -2)} in M2x2(R) () (x 4 - х3 + 5x2 - 8х + 6, -х4 + х3 - 5х2 + 5х - 3, x 4 + 3x2 – 3x + 5, 2x4 + 3x3 + 4x2 – x + 1, x3 – x + 2} in P4(R) ) (x4 - х3 + 5x2 - 8х + 6, -х4 + x3 - 5x2 + 5х - 3, х4 + 3x2 - 3х + 5, 2х4 + х3 + 4x2 + 8х} in P4(R)B) Set-7) equal to-g(x) >Vector DjSubsttute g(x) into /(x) 18. Find the Inverse of: f(x) =x-9+3. or'm-(x-3) +9 B)/() - (x-3) +9, x 23 D)Sm-(x+9)-3, x2-9 19. Pind the inverse of y-2(x+1) -4. Ay-V2x-1 +4 C) y-V x+4 1. 2. B) y Vx+4- b) y-Vr+4 21 20. The formula for the volume of a rectangular prism is, V - /wh, where /-length, w=width. and h=height. Write the inverse of the function to find the height (h) required for the Polume(V). C). %3D B) h-Viw D) h= 1+w