Suppose V is finite-dimensional, T E L(V) has n = dim V distinct eigenvalues, and S E L(V) has the same eigenvectors as T (not necessarily with the same eigenvalues). Prove that ST = TS. (Hint: find an eigenbasis for V.)

Q: show that, The compactness of a subset vof fis Sufficient Condition for existness to a best approtio...

A: Best Approximation: An element h*∈V satisfying f-h*=infh∈Vf-h is called the best approximation of f ...

Q: Write down the following statements. (a) pAq (b) pA (c) qVs

A: Since you have posted a multi subparts question according to guildlines I will solve first three que...

Q: 2- 5s b) F(s)= (s – 6)(s² +11)

A:

Q: A zero coupon bond is a bond that is sold now at a discount and will pay its face value when it matu...

A: Given that: Face value of the bond = $15000 Mature time = 28 years  Buy price = $6000 To determine...

Q: EU(Member of Coalition|Loyal) =x+) EU(Member of Coalition|Defect) = 1 *++a-x»] W Remain Loyal if : ī...

A:

Q: 2. If you know (1 – a.0 s a s 1 * f(x) cos ax dx = 0 ,a>1 Find the value f(x)!

A:

Q: The alpha level .001 has a corresponding z score of t.002 O True O False

A: Data Given in Question:Alpha level = α = 0.001 Corresponding Z score of ± 0.002  

Q: 1. Let f(æ) = { 3æ° /1 – 2a³ x3 – 3x if a 0 Evaluate f(x)dæ 2. Find F' (x) if F(x) = S VE² + Idt. · ...

A:

Q: (8) The trace and determinant of positive semidefinite matrices are numbers. nonnegative real

A:

Q: Problem 7. Let Q(3, 1, -6) and let I be the line passing through the point Q and perpen- dicular to ...

A: We have to find the equation of line L.

Q: For the given laplace domain functions obtaion the inverse lapce transformations a.k.a the time doma...

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first quest...

Q: • Use the fourth-order Runge-Kutta method with 0.5 to approximate the solution to the initial- value...

A: Given differential equation is y'=e-x/10cosx-110y Let f(x,y)=e-x/10cosx-110y with initial condition ...

Q: Describe the set of points z in the complex plane that satisfies | z + 1 - i | = 1. please show ste...

A:

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =...

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: r= 1+ 2 sin e.. Roughly Sketch the polar curve

A:

Q: Below is the equation of a conic section such that the ordered pair (Fx, Fy) corresponds to its focu...

A: Given equation of the conic is 15x2-y2-210x-8y+779=0 which can written as 15x-72-y+42+60=0⇒y+422152-...

Q: Consider the following. f(t) = t2(3t2 − 10t + 7) (a) Find all real zeros of the polynomial function...

A:

Q: dx + 2x – 3y = t dt

A:

Q: P3 (coordinates and basis) Let M = d f:a = 2f,b = 2g + h, c = 3g – i, d = g + i, e = 3h e h i. a) Wh...

A: It is given a vector space M with some restrictions in it. In part (a) first we find the maximal dim...

Q: Colleen's office equipment is depreciating at a rate of 9% per year. She paid $24,500 for it in 2009...

A: The exponential growth or decay is described using the equation: f(t)=a1±rt, where a is the initial ...

Q: 2. Find the equation of the normal line to the graph of e" tan(ry) – In(r - 3y) = sin (7x) %3D at th...

A:

Q: 3. Consider the following system of linear equations: x + 2y – z = -1 2.x + 2y + z = 1 3x + 5y – 2z ...

A:

Q: Problem 1: For the function f(x) = v1+x, (a) Find the Lagrange interpolating polynomial for f(x). le...

A: Iteration is a process to find a function such that it passes through the given data  (x0 , f0) + (x...

Q: Using ɛ-6 argument, prove that f(x) = x-[x] is continuous at all x ERexcept the integers. (Note: [x]...

A:

Q: 12. Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined b...

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball...

Q: Solve the following recurrence: T(n) = 4T(n/2) + n²lgn

A: You need to solve using masters theorem.

Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

A:

Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

A:

Q: Using a proof by contradiction and the well-ordering property, prove Vr E R, if 2 < r, then Vn E N, ...

A: Every nonempty subset of natural numbers has a smallest element, i.e, if B is a nonempty subset of N...

Q: (a) Is Rolle's Theorem applies for the function f (x) = cos(sin-1x) on the closed interval [-1,1]? I...

A:

Q: Consider the solid Q that is generated in the first octant by the surfaces S1: X + y = 4, S2: y +z =...

A:

Q: ) Suppose that the squared matrix A is symmetric and all its eigenvalues are (a) different. Show tha...

A:

Q: Find the unknown values for triangles with given parts. a = 385.4, b = 467.7, c = 800.9 a C O A = 18...

A: Solution:-

Q: Write the number 1 + i/2 - 3i in standard form a + bi. please show steps

A:

Q: What is the relationship of golden ratio to the Fibonacci numbers?

A:

Q: (a) Use the differential equation to show that any solution is increasing if m < P < M and decreasin...

A:

Q: FOLLOW(A) is the set of terminals that can come after non-terminal A, including $ if A occurs at the...

A: Given: FOLLOWA is the set of terminals that can come after non-terminal A, including $ if A occurs a...

Q: 4. Calculate Fourier transform : for a >0 r(t) = e-a'u(1)

A:

Q: 2. Consider a square ABCD and an equilateral triangle BCE in its exterior. Let F be the midpoint of ...

A: Given that ABCD is square and BCE is an equilateral  triangle.we have to prove that ED is the angel ...

Q: ing False-Position Method, find the Root of the following equation: - 3. x = 0 for the interval (0.5...

A:

Q: Q2). Study each of the following in terms of being finite - countable - finite - then find the max, ...

A:

Q: The volume of a section in a thread is given by=V = 4Sinx(1 + Cosx). What is the value of x that giv...

A:

Q: Consider the surface shown in the following figure: ZA y Let h, k, r, m, t E R. A general equation c...

A:

Q: if x 0 Evaluate , f(x)da Let f(x) = %3D 3x -

A:

Q: ind bounds on the real zeros of the polynomial function. f(x) = 13x + 13x -x - 52x- 52 The lower bou...

A:

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, xz ...

A:

Q: O A planar triangulation is constructed from a planar graph, and adding edges without edge intersect...

A: We will be solving Q.2 as mentioned. A planar triangulation is constructed from a planar graph and a...

Q: [10] Find the standard matrix representation of the linear transformation from R? into R² that corre...

A:

Q: Problem 6. Let P(1, -2, 4) and v = (3, 1, –5), and let l be the line passing through P and in the di...

A:

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0 ...