Prove that ||ư + B|| = ||T|| + ||B|| if and only if i = kủ. %3D

Q: 9. Suppose g(u) = | V1+t³dt. Find the value of (g¬1)'(0) if it exists. If it does not exist, explain…

A:

Q: n -r Prove that („",) : r+1

A: Combinations: Combination is the selection of n items taken r at a time is

Q: Find the value of k such that A is singular. 1 0 5 3 -1 0 2 k k =

A:

Q: 6. Suppose that {a,} satisfies the hypothesis of Leibniz's Theorem. Use the proof of Leibniz's…

A:

Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

A: Using complex properties.

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

A:

Q: Find the value of k such that A is singular. 1 0 4 5 -1 0 3 3 k k =

A: Topic:- Matrix

Q: Let n E Z. Prove that if 3/ (2n² + 1), then 3 | r n.

A: Solution:     Let 3 does not divide n      =&gt; n = 3k ± 1 for some integer k.       =&gt; 2n2 + 1…

Q: ?, R(A)IN(A*)

A:

Q: 3. Find two elements a and b in Z25 such that a and b are units, but a +b is not a unit. Justify…

A:

Q: 2. Show that A is Hermitian if and only if (|A|) ER for all |t).

A: The given question is related with functional analysis. We have to show that…

Q: diverges because an > 0. for all n 2 1. 2n + 1 True False

A: Given: The statement "an=n2n+1diverges because an&gt;0 for all n≥1." To determine: Whether the given…

Q: Find the value of k such that A is singular. 1 0 3 4 -1 0 2 4 k k =

A:

Q: (2 3) Let A = Verify the Cayley-Hamilton theorem. Use the theorem to express 1 2 A² and A3 as linear…

A: The given matrix is A=2312. Cayley-Hamilton theorem: Cayley-Hamilton theorem states that, "Every…

Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

A:

Q: Prove or give an counterexample to the statement that for any neZ+ and aeZn, the equation +n X = a…

A:

Q: The characteristic of Z5[x]/ is O 3 5

A:

Q: Let S= (-2, 3]U(4,5). The largest possible value of E SU such that Select one:

A: Given: S = {-2, 3} ∪{4, 5}   To find:  The largest possible value of ε &gt; 0

Q: Show that an is decreasing. %3D 2n +1 1.

A:

Q: Prove that for all positive integers n.

A: To prove for all positive integer n ∫01(lnx)ndx=(-1)nn!

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: Find all values of n such that y = xn satisfies x2y" - 12y = 0

A: To solve the equation x2y''-12y=0, we first need to find y''. y'' can be obtained by differentiating…

Q: Find the the fellowing ODE 's general Solution of ODE'S x³ - X %3D

A: Given ode xy'+4y=x3-xy'+4yx=x2-1

Q: Prove e^z1/e^z2 = e^(z1-z2)

A:

Q: O Finite fields Use Gaussian elimination, by hand, to seve the following system of equations, mod 2…

A: Solve the following

Q: Prove that P(Ø) = 0. Hint: Let A, = Ø for all i in equation (1.3.3).

A: Consider that

Q: 7. (a) Find all the values of z such that e = 1+ i.

A:

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1+ Z2| < ]Z1] + |z2|

A:

Q: Find the value(s) of k such that A is singular.

A: A matrix is singular if its determinant value is zero. So we find the determinant value of the given…

Q: Find all values of z such that cosz = 4.

A: We find all values of z such that cos(z)=4

Q: Find an explicit formula for s, if so = 1 and %3D Sn =2+2s0 + 2s1 +... +2s, 2+ Sn-1, Vn >1.

A: Generating Functions for a sequence a0, a1,a2,………an,……………… is an infinite series of the form ,…

Q: h2 |w(x) = Let h = x1 – xo, and w(x) = (x – x1)(x – xo). Proof that max %D 4

A: Let w(x)=x-x1x-x0 where h=x1-x0Prove that wx=h24.

Q: (a) Let E = {q € Q : V2 < q< 4}. Find sup E, inf E, E, and min E if they max exist.

A: The given problem is to find the Sup E , Inf E , Max E , Min E for the given set E. Given set E ={ q…

Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: (iii) Prove that there is a constant C such that 0(2º) 1.

A:

Q: f(2) = x-4I satisfies the hypothesis of Rolle's Theorem on 0, 8. [0, 8]. Select one: a. True b.…

A:

Q: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

Q: Formally prove the T(n) = (5n – 4)° is O(n³). Show all work and all steps to receive full credit.

A: Order: T(n)=(5n-4)3 T(n)=(5n)3-3.(5n)2.4+3.(5n).(4)2-(4)3T(n)=125n3-300n2+240n-64

Q: Find the value of k such that A is singular. 0 3 2 -1 0 L 3 3 k k =

A:

Q: Use Euler-Maclaurin's formula to prove that E n² = "(n+ 1)(n +2) 6. %3D 1

A:

Q: Q2) let A = [ 1 find e4t using Gauss-Jordan method.

A: First we will find the eigenvalues and corresponding even vectors of the matrix by Gauss-jordan…

Q: Find the value of k such that A is singular. 1 0 6 4 -1 0 6 2 k

A: Given. A is a 3X3 matrix. We need to find the value of k for which the matrix is singular. Singular…

Q: Find the value of k such that A is singular. 0 4 6 -1 0 4 2 k k =

A:

Q: 6. Inductively prove that B(0) = 0 for all n. Conclude that B(2) is C° function. %3D a

A: We prove the above theorem by induction. We have to prove that Bn0=0 ,∀n...1 Take n=0 then, Bn0=B0=0…

Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let:

Q: Find the value(s) of k such that A is singular.

A: to find the value of k

Q: 1. Let A = and B = For what values of t is 2A +B invertible?

A:

Q: Let A={(-1)" Find sup A and inf A. Provide some explanations how you got their values or why they…

A: