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Question: (a) Show that if two matrices A, B ∈ Hn×n, n ≤ 3, have the same minimal polynomial, then they are similar.
(b) Show by example that the statement in (a) fails if n ≥ 4.
(a) Show that if two matrices A, B ∈ Hn×n, n ≤ 6, have the same minimal polynomial and the same geometric multiplicity for every eigenvalue, then they are similar.
(b) Show by example that the statement in (a) fails if n ≥ 7.
Suppose that G is a forest Consisting of k trees T1, T2, ..., Tk. Furthermore, suppose that Ti has order ni, for 1 Is the n-dimensional cube Qn Hamiltonian? Prove your answer.
On Monday, the high temp was 20c. The low temp was -15c. What temp is halfway between the high and the low?
Do not evaluate the integral. Include a graph of the bounded region, with a labeled slice. What are the dimensions (length and witdth) of the slice? What is the radius of rotation for the slice?
We want to design an electric space heater to operate from 120V. Two heating elements with resistances R1 and R2 are to be used that can be operated in parallel, separately, or in series. What intermediate power setting is available
PARKING FEES The fee charged per car in a downtown parking lot is $2.00 for the first half hour and $1.00 for each additional half hour or part thereof.
Space Constrained Inventories, A grocer has exactly 1,000 square feet available to display and sells 3 kinds of vegetables. The space consumed by each kind of vegetable is proportional to its cost
What type of growth pattern is represented here: 5x10^3, 1x10^4, 2x10^4, 4x10^4, 8x10^4?
The rim on a basketball hoop has an inside diameter of 18.0 in. The largest cross section of a basketball has a diameter of 12.0 in.
Derive the Boolean Expression and construct the switching circuit for the truth table stated
Let (r,θ) be the polar coordinate, show that Δu=urr+1/r∗ur+1/r2∗uθθ. In particular, if u=f(r) is a harmonic function, show that u=c1logr+c2
To produce x units of a particular commodity, a monopolist has a total cost of C(x) = 2x2 + 3x + 5. Find profit function P(x) = R(x) - C(x) and sketch its graph. For what level of production is profit maximized?
a. Determine the time at which the mortar is at its maximum height. Round to 2 decimal places. b. What is the maximum height? Round to the nearest meter.
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