Problem B. Consider the linear transformation T: R₂[x] → R₂[x] given by T(a+bx+cx²) = (a - b-2c)+(b +2c)x+ (6 +2c)x² (B1) Is T cyclic? (B2) Is T irreducible? (B3) Is T indecomposable?
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I do not need the copied image from other answers, I need the explanation for the question asked please.
![Problem B. Consider the linear transformation
T: R₂ [x] → R₂ [x]
given by
T(a+bx+cx²) = (a - b-2c) + (b+2c)x+ (b+2c)x²
(B1) Is T cyclic?
(B2) Is T irreducible?
(B3) Is T indecomposable?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae19e8bd-5915-473c-8a03-9ac053dffb7e%2F7de283f6-3a03-4d45-9e6f-7b3cffd1f221%2Fcv731w_processed.jpeg&w=3840&q=75)
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- Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b + 2c)x + (b + 2c)x2 1) Is T cyclic? 2) Is T irreducible? 3) Is T indecomposable?Find the linearization L(x) of y=e10xln(x) at a=1the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows: dA/dt=2A=0.01AL dL/dt=-0.5L+0.0001AL a) find the two critical points of the predator-prey equations b) use the chain rule to write dL.dA in terms of L and A c) suppose that at time t=0, there are 1000 aphids and 200 ladybugs, use the Bluffton university slope field generator to graph the slope for the system and the solution curve. let 0 be less than or equal to A who is less than or equal to 15000 and 0 is less than or equal to L which is less than or equal to 400.
- Two interacting populations of hares and foxes can be modeled by the recursive equations h(t + 1) = 4h(t) − 2 f (t) f(t+1)=h(t)+ f(t). For each of the initial populations given in parts (a) through (c), find closed formulas for h(t) and f (t). a. h(0)= f(0)=100 b. h(0)=200, f(0)=100 c. h(0)=600, f(0)=500determine the critical point x = x0, and then classify its type and examine its stability by making the transformation x = x0 + u. 13.(0−βδ0)+(α−γ);α,β,γ,δ>0Prove that the transformation z = y^1−n reduces the equation dy/dx+P(x)y = Q(x)y^n to a linearequation in z and x. Hence, solve the initial value problem dy/dx+xy = x/y^3; y(0)=2.
- d) Prove that the transformation z = y^1−n reduces the equation dy dx+P(x)y = Q(x)yn to a linear equation in z and x. Hence, solve the initial value problem dy/dx + y/x=x/y^3If {~v1,··· ,~vr} is linearly independent and T is a one to one linear transformation, show that {T~v1,··· ,T~vr} is also linearly independent. Give an example which shows that if T is only linear, it can happen that, although {~v1,··· ,~vr} is linearly independent, {T~v1,··· ,T~vr} is not. In fact, show that it can happen that each of the T~vj equals 0.For Question 3 of task one it states that the transformation matrix for this opertator is invertible. It is not however, this is singular. Does that change Q3 on task 1?