O Let (R, +) is aring. and f:R>R defind as XER Show that f is isomorphi'sM and is said tobe identity isomorphism. Let (e>+) is aring of complex numbers and Mz be aringofX2 matrices aud g, &–DM, défined as follows- ollarb}= ( isemesphim or not. show that whether gis -ba) ab

Q: In to which point in the complex W-plane is the point (2, 3) of the complex z-piane mapped by 2z-1…

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Q: list any Product. ExPlane it bofedls way two Proparties of as in n cun your and Provide it withh…

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Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

Q: 9. Represent the following relations on A = {1, 2, 3, 4, 5, 6} using a matrix and a digraph. (a) R =…

A: Given that ,  A = { 1,2,3,4,5,6}

Q: If L and U are invertible, then (LU) – Find A from the given LU factorization: 9 -27 7-14 96 = -63…

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Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: MR₁ = To Let R₁ and R₂ be relation on a set A represented by the matrices 50 1 07 1 1 0 1] 0 1 0 1 1…

A: The objective of the question is to find the matrices that represent the union, intersection, and…

Q: A) .3 Find the determinant of -21 B) 63 1 2 4 -1 -1 '1 -1] 1 -1 3 -2 3 1 3 -2 -11 C) 21 d) -42

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Q: Let 1 2 A = 3 6 Is A invertible? Explain your answer.

A: To verify is the given matrix A is invertible Or not.

Q: How many possible Jordan canonical forms are there for a linear operator T: C6 C6 with…

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Q: Q10\ Express -2+j, 3+ j2, and 1-j2 in polar form and apply DeMoivre's (1- j2) (-2+ j)(3+ j2)*…

A: The given complex numbers are -2+j,  3+j2,  1- j2

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

A:

Q: We proved the following theorems in previous group work. Write the dual of each of the theorems and…

A: To find- Write the dual of each of the theorems and prove that each dual statement is true. A ∩ B ∩…

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: i) ii) (AB) = B*A', ii)AA)* = TA', (A+B)* = A* + B', %3D %3D %3D where A is a complex number and At…

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Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: Find projvu and projuv. Use the Euclidean inner product. u = (7, -5, 1), v = (1, -1, 0) (a) projvu…

A: The given vectors and .We have to find the values of the projection,a) b) .

Q: a;jA = Aô;*, Show that where A is a determinant of order three and A" are cofactors of a.

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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: 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: Express -2+j, 3+ j2, and 1-j2 in polar form and apply DeMoivre's Q6/ (1 – j2) theorem to evaluate 2+…

A: Any complex no. can be written in polar form as : →a+jb = a2+b2∠tan-1ba According to DeMoivre's…

Q: Let { = fo + ū and 7 = no + ở so that quaternion multiplication gives §n = £ono + £oð + noũ + ữỡ.…

A: are ξ,η are quaternion numbers So, Let  ξ=ξ0+iξ1+ξ0+Iε2+kξ3 u→=iξ1+ξ0+Iε2+kξ3 and η=η0+iη1+Iη2+kη3…

Q: Prove that rotations, reflections, and composites of rotations and reflections are orthogonal…

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Q: Let R²-be a inear transformation that maps. The image of Aus [1 to and maps v into Use the fact that…

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Q: 3 2 O -1 2 4 e -1 6 -1 -2 3 یه -S 3 -8

A: Gauss Jordan row reduction method is used to find the solution of the system of linear equations in…

Q: What is the coefficient What is the coefficient of rx3x3 in (x₁ + x2 + x3 − x4 - x5)⁹? 1 13 of 2¹3…

A: To find the coefficient of x14 x32 x43 in (x1+x2+x3-x4-x5)9 we will use binomial theorem.  The…

Q: 29. Let the characteristic polynomial of a matrix be p(1) = ² +62+9. a) What are the dimensions of…

A: Use the properties for eigen values

Q: Evaluate the determinant of the ナhc given mantrix using 91 92 93 result b2 bz = 5. C3

A: Given that:      a1a2a3b1b2b3c1c2c3=5

Q: 9) What transformation do you apply to get from figure B to figure C?" (x.y) - (x-2. y-3) O)-(xy-3)…

A: Here transformation is 3 unit left and 2 unit down is using for Figure B to Figure C Sothat: (x,y)…

Q: R^n×n is invertible, show that AB is similar to BA for all B ∈ R^n×n.

A:

Q: Find projvu and projuv. Use the Euclidean inner product. u = (-1, 2, 1), v = (1, 2, 1) (a) projvu…

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Q: y)(Ty → Wy) - Hv)) → Ia

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Q: * Suppose the mbrxP. 4x4 peraubibun mabrx with even numberof permutahion, Find bhe maxinum…

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Q: Without using determinants, show that {(2, –x,,3x²,x³} is a basis for Ps then find dimension for P3

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Q: 4 1 0. 5 -3 -1 6- 4- 2. 2.

A: To find the solution by using cramer's rule

Q: (a) Let V be R², and the set of all ordered pairs (x, y) of real numbers. Define an addition by (a,…

A:

Q: ) Let B = {1,1+x, 2+x+x2) and D Pn is the set of polynomials of degree n). a) (1+x, 1-x) be bases of…

A: