The linear transformation y=a + Bx that maps x in the interval (-1, 1] to y...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
10.10 If A is an 'n x n matrix, and x is an n x 1 vector, then the linear transformation y = Ar maps* n to·m, so the linear transformation should have a condition number, condAx (x). Assume that l a subordinate norm a. Show that we can define condar (x)-[All Irl/IArll for every x 0. b. Find the condition number of the linear transformation atx [ - 2 using the oo-norm ng the oo-norm. T-3 2 1 .12...
7. Consider the fractional linear transformation that maps -1 to -2i, 1 to i and i to 0. Determine the image of the unit circle EC 1 the image of the open unit disk (z EC<1), and the image of the interval [-1,1 on the real axis Illustrate with a sketch
Question 7 Determine whether the linear transformation T is one-to-one and whether it maps as specified. 2 + 3x 3) T(X 1, X 2, x 3) = (-2x 2 - 2x 3, -2x 1 + 8x 2 + 4x 3, -X 1 - 2x 3,3x Determine whether the linear transformation T is one-to-one and whether it maps R 3 onto R4. Not one-to-one; not onto R4 One-to-one; onto R4 Not one-to-one; onto R4 One-to-one; not onto R4
(c) please Tz that 1. Find the most general linear fractional transformation w = maps the region A into B : (a) A = {l-1 <1}, B = {Im w >0} (6) A = {lz| <1}, B= {Rew >0} (c) A = {]z – al < R}, B = {Rew 5-3}
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Consider the transformation T[x y] = [x + y y^2] a. Is T a linear transformation? b. Is the range of T closed under addition? c. "" scalar multiplication? 10. Consider the transformation T1yHyy (a) Is Ta linear transformation? (b) Is the range of T closed under addition? (e) Is the range on T closed under scalar multiplication?
4) The linear transformation L defined by L(p(x)) = p'(x)+p(0) maps Pinto P. a) Find the matrix representation of L with respect to the ordered bases {1,x,x} and {1, 1-x}. 6 b) For the vector, p(x) = 2x + x - 2 (i) find the coordinates of L(p(x)) with respect to the ordered basis{1, 1-x}. , using the matrix you found in a). Remember to use the coordinate vector of p(x) with respect to the basis {1,x,x"}. (ii) Show that...
z+1 The linear fractional transformation shown below is related to w = u + jv and z = x + jy w= z-2' a. Calculate the curves that the lines v = constant maps to in the x-y plane, b. Calculate the curves that the lines y = constant maps to in the u-v plane, c. What is the line in the x-y plane that maps to a line in the u-v plane?