[1 1 1 -3 1 -3 -4 [1 -1 Find the QR factorization of A = 1

Q: -1 -2 -3 2 3 5 6 1 Let A = 1 Compute A-1 using adjoint.

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Q: Show that the Newton divided-difference polynomials 3 - 2(х + 1) + 0(х + 1)x + (х+ 1)x(х — 1) аnd…

A: Given,

Q: 1 - 1 2 T-1 1 0. and B= 5 Find x such that Let A = -7 1 3 - 2 - 2 - 2 14 - 57 AB = 27 - 32 3 %3D - 5…

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Q: Let X = [-1 -1 1] and Y = [0 1 2] consider -1 -21 [a11 XTY = | -1 -2 а32 азз. where X' denotes the…

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Q: 4. Consider the complex number w = 3cis (). For which value(s) of k is z - w a factor of the…

A: We will use remainder theorem to find the value of k. Remainder theorem says that if x-a is a factor…

Q: Question 2 Given the points (-1.-3) , (0,1), and (1,1). The Lagrange interpolating polynomial can be…

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Q: -1 -2 Find the characteristic polynomial of A %3D 4 3 O 2 – 51 – 2 O 22 – 4X – 5 OX2 – 21 +5 OX2 +…

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Q: 2.1 Find the appropriate Lagrange interpolating polynomial using the following data table 0 0.5 1…

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Q: Show that 1/2 1+ 72 2 1. i%3D1 Xi n-1

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Q: 1 1 0 k- 4 -k + 5 is not diagonalizable over C. k (Enter your answers as a comma separated list.)

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Q: The ________ ________ ________ states that if f(x) is a polynomial of degree n (n > 0), then f(x)…

A: Consider the statement, The ________ ________ ________ states that if f(x) is a polynomial of degree…

Q: 4. Consider the complex number w = 3cis (5). For which value(s) of k is x – wa factor of the…

A: I am going to solve the given problem by using some simple geometry to get the required result.

Q: A factor (x − a)k, k > 1, yields a ________ ________ x = a of ________ k.

A: x=a is a repeated zero of multiplicity k, when we have (x-a)k.

Q: (b) Determine the Z-transforms of the following expressions 6n+5(n+1)-4(-8)" (i)

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Q: 1 0 -11 1 2 1 Let A = Determine the QR-factorization of A. 1 1-3 1 1

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Q: Use the inverse form of the first translation theorem to determine the power of e. 2! %3D (S-5)° -5t…

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Q: a) What is the generating function for {ak}, where akis the number of solutions of x1 + x2 + x3 = k…

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Q: Find the values of k for which A is invertible. а. [1 2 4 A=3 1 6 k 3 2

A: Given that: a. A=124316k32b. A=120k1k021

Q: Let 1 2 -1 P = 0 1 0 0 1 -2 4 A = 0 -1 and 0 -1 1 Given that P diagonalizes A , then compute each of…

A: A=1-240-1000-1 and p=12-1010001

Q: 223+-5 -j Suppose z1 = 2+ j, 2 = 3- j2 and z3 = -+j Evaluate %3D 2-a+3-j

A: Substitute the given values of z1,  z2, z3 in the given expression and simplify.…

Q: B. Find the coefficients specified in each item. 2. a² in (6 - 1/2a)6 a4 4. k4 in (3k – 21)¹2

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Q: Find the string that has this generating function: a) (1− x)−3 b) (1+2x)−4 c) 1/(1 −3x)3

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Q: Find the coefficient of a' in the expansion of: (a) (1 – x)-4x (c) x²(1+ x²)*(1– x)-3 (b) (1 – x)-2x…

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Q: nn MEGMar(1-|-.0) i=1 j=1 i=1 j=1 = GĞMar(1-r- al.0) + GÖMar(1–|h- 2|,0) + ciğMar(1- |21 -23,0) +…

A: Yes, because When you are assuming C1 = i , C2 = 0, and C3=0, Then summation will be -1 which are…

Q: 2. Determine tz , t4, and ts for the recursion formula listed below. A) t = 1, t= 3, 4-2 tp-1 -…

A: By using the given formula putting values of n.

Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: -1 1 0 B 2 4 4 0 3 2 1 1. Let A= and C Let a =4 05 -2 -2 -6 5 -2 2 and 3 = Compute the following

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Q: 5. Suppose A = PDP¯1, where P is 2 × 2 and D = 9I. Let B = 51 – 3A+ A². Show that B is…

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Q: 4. The field of quotients of (Z2, +2)-2) is (a) Q2 (b) Z2 (c) Z4 (d) Zg

A: Field of quotient

Q: Show that A and B commutes: * 2/3 -1/31 1/5 7/15 -1/5 1/15. 1 1 0. 21 1B =|-3/5 2/5 2 4. 3 %3D -1 ]

A: Given A=112231-124, B=230-13-352515715-15115

Q: -2 Find the Schur triangularization of 4= 1 1 3 -

A: Explanation of the solution is given below...

Q: T-F If gcd(3a, 3b) = 6 then a and b must be relatively prime..

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Q: -4 4. 2 -2 and P=0 1 0 1 Given that P diagonalizes A, then compute 1 Let A = 0 -1 0 %3D 0. -1 0.…

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Q: 1 2 Find the characteristic polynomial of A = 3 4 O 2 – 51 – 2 O12 – 4X – 5 O12 – 21 + 5 Ox2 + 3A +2…

A: The matrix is given by A = 1234 To evaluate : The characteristic polynomial.

Q: x3 + (2i – 1)x³ – 2ix – 5 a = 1- i -

A: Given: The given polynomial is x5+2i-1x3-2xi-5 a=1-i into binomial.

Q: Let 1 -1 8 -3 -5 2 -1 , and B = 1 %3D %3D -2 1 4 -7 Compute A-1, (BT)-1 and B-1A-1. What do you…

A: A=1-1102-1-213, B=8-3-50124-76 Expanding the determinant of A, B along column first…

Q: (1/6)æ° + (2/3)x³ + (4/3)x* + (7/6)æ³ + (5/3)x² + Use part (b) to prove that g(x) (2/3)x + (5/6) is…

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Q: [ Let A 1 -2 10 1 1 -5 -1 0 and P 1 |0 -1 1 Given that P diagonalizes A, then compute each of the…

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Q: 8 1 4 9 1 1 1 4 7 10 3 7 7 11 1 What is the mode? If there is more than one mode, enter your answers…

A: Mode: mode may be defined as the maximum frequency of the observation is called mode.

Q: 1- The Newton's divided interpolating polynomial on x, = x,-1 + 0.25, Vi=1,2,3 , xo = 0 given by…

A: Given: P3x=fx=1+4xx-0.25+163xx-0.25x-0.5, xi=xi-1+0.25 ∀i=1,2,3, x0=0

Q: Find the canonic analytical expression of the following quadratic form q: R³ → R, q (x) = 6x,²+x,² –…

A: Given quadratic equation is…

Q: Let A = -1 0 and P 1 -1 1 | Given that P diagonalizes A, then compute each of the following powers…

A: We are asked to find the given matrix.

Q: Question 2 Prove that the polynomial f(x) = x2 + a2", n € N, a E R\ {0} is not divisible by g(x) =…

A: Factor theorem: The polynomial f(x) has a factor x-k if and only if f(k)=0. Given: f(x)=x2n+a2n,…

Q: 2 17 1 12 7 15 2] What is the coefficient of X in the characteristic polynomial of the matrix A =…

A: Given matrix 5211127152Form a new matrix by subtracting λ from the diagonal…

Q: (2.5) Find another representation in which a. r is negative and °<0 < 2n. b. ris positive and -2n <0…

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Q: 5. Compute for the product of the complex coardinates :(3, 1)(3, - 1) a. (2,1) b. (1,1) c. (3,1) d.…

A: The given problem is to find the product of the given complex coordinates, We have to use product of…

Q: 1 2 Find the characteristic polynomial of A= 3 4 12 – 51 – 2 O12 – 4X – 5 O 2 – 21 + 5 O 12 + 3A + 2…

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Q: Therefore n-1 ( fsi+4P + föi+3h foi+3P + fei+2h ) (foi-19+ fei-2k , feiq + fei-1k Tên-3 = k| i=0…

A: Given : In Theorem 4,                 fmm=-1∞=1, 0, 1, 1, 2, 3, 5, 8, ......... We need to explain…

Q: Use the Factor Theorem to prove that x + c is a factor of xn + cn if n ≥ 1 is an odd integer.

A: Let f(x)=xn+cnNow take,x+c=0i.e.x=-cNow, considerf(-c)=(-c)n+cn          =0          (Since, n is an…

Q: Given: z = 6 + 7i Calculate the following: 1) z-4

A: z=6+7i1z=16+7i×6-7i6-7i=6-7i851z4=(6-7i)452200625=(-13-84i)252200625=-6887+2184i52200625