2. Determine whether the following equations are linear in r, y and z: justify your answer.
answer, determine whether the function linear transformation T: R² M₂,2 define as TG y z)=Rz xty Loc-32 x-y ST: P - R defined as I (at boct (x²) = a-2b +36
Problem 3 Determine whether each of the following system is memoryless, stable. Justify your answer time-invariant, linear, causal or (a) y(t)r(t -2)+x(-t2) b) y(t) cos(3t)(t) (c) y(t) =ar(r)dT d) y(t)t/3) (e) y(t) =
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
Determine whether the multiplicative group Z∗24 is cyclic or not. Show work to justify your answer.
By justifying your answer, determine whether the function T is a linear transformation. (a) T : R3 → M2,2 defined as x+y T(x, y, z) = x – 3z x - y (b) T : P2 → R defined as T (a + bx + cx?) = a – 2b + 3c. +
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
Page 2 of 7 2. For the electromagnetic waves defined by the following equations,(6 pointsy a) Find po for linear and circular polarization cases. b) If ,-00, determine the time-average Poynting vector, ie. g.(z)-0 c) Determine the potential mode of operation and justify your answer .5 Re(E.*R,*) Page 2 of 7 2. For the electromagnetic waves defined by the following equations,(6 pointsy a) Find po for linear and circular polarization cases. b) If ,-00, determine the time-average Poynting vector, ie....
linear algebra 2. Which of the following subsets of Rare actually subspaces? Justify your answer in terms of the definition and properties of subspaces. (a) The vectors [x y z]" with x + 2y -z = 0. (b) The vectors [a b c]" with a + b + c = 3. (c) The vectors [a+2bb-3b]' where a, b are any real numbers, (d) The vectors [pr] where q.r are any real numbers and p20.
Determine whether the linear transformation is one-to-one, onto, or neither T: R^2 -> R^2 , T(x,y) = (x-y,y-x)
Determine whether the following statement is true or false. Justify your answer. Let a and b be real numbers. The following system of equations can have exactly two solutions. 2x+7y=9 3x-4y=b