Find the value of x for which A is not invertible: x – 1 A = 1 x + 2

Q: Prove that if A is invertible and AB = 0, then B= 0. Give a counterexample to show that the result…

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Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

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Q: Let A and B be two sets and f be function. f: A B.Assuming the function f is invertible, what is the…

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Q: The Maclaurin expansion of f (x) = e¯7× is %3D

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Q: The expanded form of the differential operator D(xD-1) is A XD²+1 B XD² C XD²-1 (D) XD²-D

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Q: Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2=…

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Q: verify that the given function is in the kernel of L. Q. y(x)=xe2x, L = D2−4D+4

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Q: The linearization at a = 0 to V6+ 5x is A+ Bx. Compute A and B %3D A = %3D B = %3D

A: Consider the given: Let fx=6+5x    at x=af0=6+50f0=6+0f0=6

Q: (b) 1 = -4 - 4- 2.

A: Given that

Q: a) Let f: Z Z be such that f(x) 2*x. Is f invertible, and if so, what is its inverse?

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Consider the functions fi(x) = 6x, f2(x) = 3x², and f3(x) = 12x + 3x². A) If fi and f2 are solutions…

A: Use Principle of superposition to solve this differential equation.

Q: (a) Prove that if A is invertible and BA = CA, then B=C. (b) Give a counterexample to show that the…

A: Given:         Part(a):Since A is invertible then A−1 exist.Now,BA=CA(BA)A−1=(CA)A−1…

Q: Let A = → Rm be (a;j)ij be an m xn matrix of real numbers, and let f : R" defined by x2 X2 f = A…

A: I am solving this in step 2

Q: Show that the operators Ix=x 0x = 0 Tx (t)=n't & are Linear. 6

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Q: Find the value of x for which A is not invertible: x – 1 | 1 A = x2 x +2

A: Consider the given matrix. A=x-11x2    x+2   If A is a invertible matrix then A=0

Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

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Q: Consider the D-operator P(D) = mD² + 2kD +¢, where m and c are positive. If -c/m < k< 0, then

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Q: Prove that if A is invertible and BA = CA, then B = C.Give a counterexample to show that the result…

A: Given: A is invertible and BA = CA  To prove: B = C

Q: Let f : A → B and g : B → C be bijections. Prove that gof is invertible and that (g o f)-1 = f-1 o…

A: Problem based on function.

Q: The expanded form of the differential operator D(xD -1) is XD² – 1 A В xD² (c) xD² +1 C D xD² – D

A: To find the expanded form of differential operator, D(xD-1)

Q: () Let z = x + iy. Find Im and Im 2 in terms of x and y. Im Im z2 ||

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: Let xj = xo + hj for j = 0, 1, 2. Use the quadratic polynomial interpolating f at those nodes to…

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Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: Let T: X→→→→→ Y be a linear operator and dim X = dim Y=n<∞. Show that R(T) = Y if and only if T¹…

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Q: Find the value of the constant 6 for which J is continuous at * = -1 and determin f(-1). z - 5x bx -…

A: The given function is: f(x)=x2-5x        x&lt;-1bx3-7x≥-1

Q: The linear operator T: R2 --> R2  defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?

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Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: True or false? If det(A)= 0, then A is not invertible.

A: Explanation: Case 1: If det(A) is invertible. In this case, det(A) not equal to 0 because in matrix…

Q: Find all values of kfor which A is invertible.

A: Given A=kk0k22k0kk

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

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Q: Find the positive integer A such that t²x" +tx' + t²x = λx has a nontrivial solution satisfying x(0)…

A: Hint: Substitute t=ey , t2x''=D(D-1), tx'=D-1in the given equation and calculate to obtain the…

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = 3√x, a = -8

A: Given function is fx=x3 Linearization of function is given as: Lx=fa+f'ax-a At a=-8 f-8=-83=-2…

Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of 1- 1?

A: Ix=2x-18 Now let, y=2x-18 Now to find inverse function interchange x and y, then solve for y in…

Q: Consider the following operator A : L²[0, 1] → L'[0, 1] A(f)(x) = (f(x))² + f(x). If this a linear…

A: Given, the operator  A : L20, 1→L10, 1 defind by                               A(f)(x)=(f(x))2+f(x)…

Q: a. If AER dxd satisfies A¡¡>0 for i=1,...,d, then A is invertible. dxd b. When A,BER are both…

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Q: Q3: Using Fredholm determinates, find the resolvent kernel of the kernel : k(x, t) = sin(x) –…

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Q: Suppose A and B are invertible then det(A) = det(B) %3D O True O False

A: Consider A and B are invertible

Q: 4) Find Yp, using D-operator, where Yp (e). %3D (D+1) (D-2)

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Q: verify that the given function is in the kernel of L. Q.y(x)=x−2, L =x2D2+2xD−2.

A: Given differential equation is, L=x2D2+2xD-2 and yx=x-2 To verify that the given function is in the…

Q: verify that the given function is in the kernel of L. Q. y(x)=xex, L =−D2+2D−1.

A: given that  y(x)=xex

Q: Prove that if A is invertible and AB=0, then B=0.

A: Given:

Q: Find all values of kfor which A is invertible.

A: A=k-k30k+11k-8k-1

Q: Given that f is an invertible function, if the point (x, y) lies on the graph of y = f(x), then the…

A: We have to find at which point is guaranteed to lies on the graph of  y=f-1(x).

Q: Let k be a constant number. (a) Compute (1+x + x²)*. (b) Find the linearization of (1+x + x²)k at x…

A: given

Q: The value of a' for which f : R → R, ax +7 flx) is invertible lies in %3D 2 x* +4 (а) (0, 2) (b) (1,…

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Q: Determine whether the following are linear operatorson Rn×n. L (A) = A − AT

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.