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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- Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]Identify the matrix that represents each linear transformation below. Write A, B, C, D, D or F. 20 -2 0 A = B= = 02 0 -√212 √212 (39), ^ - (² :) " - ( - ² - 2).C-( √²/2 √212) P-(-03). E-(0-²). 2 D= E= 20 and F= √212-√212 √212 √212 1. Clockwise rotation by an angle of 450 is associated to matrix 2. Counterclockwise rotation by an angle of 45° is associated to matrix 3. Clockwise rotation by an angle of 90° is associated to matrix 4. Counterclockwise rotation by an angle of 900 is associated to matrix 5. A dilation by a factor of 2 is associated to matrix 6. Reflexion about the origin and a dilation by a factor of 2 is associated to matrix Hint: Draw a vector and its image under each transformation.Explain Matrix-Valued Functions?
- Exercise 273. Show that projw is a linear transformation and that (projw)² = projw.Find the matrix A of the linear transformation from R² to R³ given by 1 0 -4 x1 + -8 x2. - 2 6 A = = T ([^]) =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.
- Consider a linear transformation T from R2 to R² for which (:) -}- T and T Find the matrix A of T. A =A survey shows that there is a linear function between population of a country and time. In the year 1980, population was 84 people and in the year 1990, population was 93 people. (i). Find the linear function between population and time(ii). Calculate from the obtained linear function, the population which the country would have in the year 2000(iii) Calculate from the obtained linear function, the population which the country would have in the year 2020If ()=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.
- Let f={(0,8),(5,0),(9,4)}. Find f(0)Let T be a linear transformation, and suppose T transformation induced by the matrix B = First component = 2 -3 ([_^)) = [²] = [₁3] Find (S07) ([¹]) 1 Second component = Suppose S is a linearFor the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A), nullity(A) A. det(A)<nullity(A)<rank(A) B. det(A)<rank(A)<nullity(A) C. nullity(A)<rank(A)<det(A) D. rank(A)<det(A)<nullity(A