Exercise 4.2.6 Let 2₁ = [1] and $22= [3 0 20 4 Verify that both are hermitian. Do they commute with respect to multiplication?

Q: If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a…

A: If A is diagonalizable and B is diagonalizable then it is not necessary for AB to be diagonalizable.…

Q: B = [3 {[9][9]} 02 4 0 56

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Q: Show that if B is an n × n matrix with entries in C and  B3=B then B is diagonalisable. Where C is…

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Q: Find two examples to demonstrate that if (a-d)2+4bc =0 then A may or may be diagonalizable

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Q: If A²=0, prove that A cannot be invertible.

A: Given,If A²=0, prove that A cannot be invertible.

Q: Let A = 1 -X -X X 1 -x X X -1 Find x such that A is invertible.

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Q: Solve the initial value problem below using the method of Laplace transforms. w" - 2w' + w = 2t +6,…

A: Given initial value problem is

Q: Q3. Determine the kernel and range of each of the following linear operators on R³: (a) L(x) = (X3,…

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Q: ITA Is a bounded self-adjoint operator on a Hilbert space н, show that |= sup {|}: xe H |x| = 1}

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Q: Display a Hilbert-style derivation of ~~P → P.

A: Hilbert - style Deductive Systems:  A Hilbert system, sometimes called Hilbert calculus,…

Q: Exercise 9.1.9 Consider the set R of real numbers. Addition of real numbers is defined in the usual…

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Q: Without expanding the determinants, 103 115 114 113 116 111 108 106 + 108 106 104 113 116 115 114…

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Q: Under what condition on the numbers m1, m2, ... , m9 do these three parabolas give a basis for the…

A: To Find: The condition on m1,m2,...,m9 for which m1+m2x+m3x2,m4+m5x+m6x2,m7+m8x+m9x2 forms a basis…

Q: Suppose I + AB is invertible. Show that I + BA is also invertible by showing that (I + BA)¯ = I –…

A: Assume that I+AB is invertible.  Then, I+ABI+AB-1=I ⋯ 1. Use equation (1) and calculate…

Q: Exercise 2. Find (4725, 3234) and [4725, 3234] using the canonical representation.

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Q: Find the inverse of the following matrix: -7 5 -6 5 -2 3 1 −1 1

A: Given matrix: We have to find the inverse of the given matrix.

Q: и %3D-2, 1] -2u = [ Ex: 5

A: Step:-1 Scalar multiplication:- Let V = v1, v2  be any vector and let  "a" be any scalar then a.V…

Q: 1. If two Hermitian operators A and B commute, show that they can be simultaneously diagonalized.

A: Given :-  If two Hermitian operators A and B commute , then they can be simultaneously diagonalized.

Q: c) Write their Jordan canonical form. d) State the dimension of their kernel. A B = = 3 -1 3 9 25 3…

A: Jordan canonical form

Q: 4.) Prove that the following statements are true when A and B are square matrices of order n and c…

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Q: Let T be abounded linear operator on a Hilbert space H. Then T, =(T +T) is Select one: O none O (T'…

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

A: To prove that if A is invertible and AB=0, then B=0.

Q: Determine whether the set [p., pa, p3] is linearly Independent in Pa, where pi= 3+x+3x²+4x3 Pa = 4+…

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Q: [o 5 Write down the quadratic form corrsponding to the matrix 5 1 -1] -1 6 2 6

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