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: 3. Let A = a. b. 1-2 3 1 1 1 Find the Null space of A. Find a basis for Null space of A. c. Find the…

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Q: А понерне об mension of each ? A= 52 Зо -1322 Ч 21 з

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Q: 1 1 -2) 13. Find the rank of A=| 2 1 |and explain why it indicates that A is (-1 -1 2 not…

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Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

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Q: A (real or complex) scalar u is said to be an nth rootof unity if un = 1. Show that if j and k are…

A: To prove this If j and k are positive integers,

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Using the scalar form of the table 1 3 2 3 1 1- - a 1 6 = 6+ a 5 4-a 2 -2 5 12 19 to determine the…

A: Step 1: Write the matrix A in scalar form. A = [[1, 3, 5, 6 + a], [2, 3, 4 - a, 2], [1, 1 - a, - 2,…

Q: Compute the value of the expression (II,3**) : (II,3').

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Q: 2. How many edges has each of the following graphs: (а) (5 рoints) К10: (b) (5 рoints) K,7; (c) (5…

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Q: Let k be any real number except 1 and -2. Show that S = 1 k is a basis for R3.

A: Given   S={11k,k11,1k1}To show…

Q: Find a basis for the ideal √(x³ - 214 + 2x² - x, x5-14-21³ + 2x² + x − 1). ស

A: We have to find a basis for the ideal x5-2x4+2x2-x,x5-x4-2x3+2x2+x-1

Q: H is a Hermitian operator in a finite dimensional inner product space V. Show that H has at least…

A: Eigenvectors: An eigenvector v of an operator T is a non-zero vector corresponding to the eigenvalue…

Q: Find a basis for the span of {[1, 3]", [-1, 3]T, [1, 4]T , [2, 1]T}

A: We have to find a basis for the span of   [1, 3]T, [-1, 3]T, [1, 4]T, [2, 1]T .

Q: 1. Let B₁ = = {-1} {[]} i) Find Rep ii) Find Rep B1 and -{[]} B2 = be two ordered bases for R² C…

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Q: | Let v₁ = (1, −1, 1, − 2), v₂ − (−1, 2, −1, 1), v, −(−2, 1, −1, 5). Determine whether {V₁, V₂, V3}…

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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: Asap show correct work and answer

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Q: -5 -1 -7 -2 Select true or false for each statement. Let A = 2 b = [4] and c = 21 1. The vector c is…

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Q: Use the field F =Z2[x]/<x2 + x + 1> to construct a (5, 2) linearcode that will correct any…

A: Consider the given field, F=Z2x/x2+x+1 Now, abbreviate the coset a+x2+x+1 with a. Then the…

Q: Which elements are invertible in Z4[x,y]?

A: W need to find elements which are invertible inZ4x,y.

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: 2 3 [+0 4 2 b = -2 Select true or false for each statement. Let A = and c = [12] 1. The vector c is…

A: The objective of the question is to determine whether the given vectors b and c are in the kernel…

Q: Let A = [1111;0101;1212;0-10-1] = [1 11 1] [0 10 1] [1 21 2] [0-10-1). Find bases for the column…

A: Given:-                    Given matrix                                           A =…

Q: Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c)…

A: The following are the rules in the Einstein's summation convention having the index notation:1) The…

Q: Explain why S is not a basis for P2. S = {1, 6x, –9 + x², 7x} O Sis linearly dependent. O S does not…

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Q: H is a Hermitian operator in a finite dimensional inner product space V. Show that there exists at…

A: Trick here is to show that H has an eigenvalue and if H has an eigenvalue then by the definition of…

Q: Show that for binary vectors, wt(u + v) ≥ wt(u) - wt(v) and equalityoccurs if and only if for all i…

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Q: Let [3³] Ai B , where B = {b₁,b₂} is a basis in R². Then 3 B 061+06₂

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Q: Q1/ Prove or disprove: A) If A is invertible and k is a nonzero scalar, then kA is invertible and…

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Q: Find bases for the null and range spaces of 1 2 3 1 1 1 A = 3 4 5

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