Let p(x) = x³ – 2x + 4 and compute p(A). 1 A = 0 -4 4 NOTE: Write the elements of the matrir exactly.

Q: 1 -1 0 2 Find a mat rix P such that P 1 0 0 2

A: consider P be any matrix having entries P=abcdgiven: P-1 1-102P=1002multypling P from right side.P…

Q: Let z = 2 – 3i and w = -3 + 2i. (a) Find z + w and z – w. -

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Q: 1 0 Find a mat rixP such that P- 0 2 | 0 2

A:

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: How did they calculate what T does to the elements of B?

A: You want to know "How did they calculate what T does to the elements of B?" We have  B=1, x, x2, x3…

Q: Let f(x) = x, the second Taylor polynomial P2(X) about Xo = 2 is: Select one: O 1+ 3x + 6x? 08-12x +…

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Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: Show that ZV-6 is not a UFD by factoring 10 in two ways. Why does this prove that Z[V-6] is not a…

A: Given, Z-6 is not a unique factor domain.To find:Z-6 is not a principal ideal domain.

Q: 3 1 Find a mat rixP such that P- 0 2 3 0 0 2

A: P-13102P = 3002

Q: Suppose X = (X1, X2, . .. , Xk) ~ Multinomial(n, p) , with p = (p1, P2, ..., Pk), prove that Cov(X;,…

A: Introduction :-  Given that X is a vector of random variable and it follows Multinomial(n,p) Where p…

Q: Find the Taylor polynomials p3 and p4 centered at a = 1 for ƒ(x) = 8√x.

A: Given f(x)=8x centered at a=1

Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

A:

Q: 18. Let xo < x, < x2, let {yo, y, y2} be given. Find the polynomial q(x) with deg(q) < 2 and such…

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Q: Let (-1,(-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions?…

A: Given, -1,f(-1)=2,(0,f(0)=5) and 1,f(1)=6

Q: The set of polynomials {1, x² + 3x“, 2x² – 7x4} is a linearly independent set in P4.

A: NOTE: Due to time limit answer of 1 is given here, for other please ask in a different question.…

Q: Find the set of all values of a for which f(x) = x° +(a + 2)x² + 3ax + 5 is invertible.

A: We know that, for function to be invertible the discriminant of its first order derivative should be…

Q: The Taylor polynomial generated around x, =Oby %3D f(x) = e*is Select one: 00 O a. k%3D0 (2k)! k* b.…

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Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: 3 0 3 0 P 1 2 Find a mat rix P such that p-l 0 2

A: According to the Question

Q: Investigate the stability of the following sys (Consider the quadratic form as lyapunor system.)…

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Q: Find ATA and AA". 2 0 1 %3D -1 4 2 (a) ATA 1 1 (b) AAT 21 Which of the products are symmetric?…

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Q: [1 0 1 2 0 -1 Find a mat rix P such that P- 0 -1 [10]

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Q: Find (a) ATA and (b) AAT. Show that each of these products is symmetric.

A: a).

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: the integret fector of the bifferentiel e qration →き x28x he is 2. O Not found

A: Consider the given differential equation xdy-ydx=x2y3dx and rewrite it again by doing…

Q: Find a mat rix P such that 30 P%= 1 2 30 0 2 1 0 OAP = %3D 3 -1] 1 0 OB P -3 1 -1 0 OcP = %3D 1 0…

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Q: Find the Taylor polinomials of orders 0, 1, 2, and 3 generated by f(x)= Vx+4 at a = 0.

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Q: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

A:

Q: 26. Determine whether the polynomial in Z[x] satisfies an Eisenstein Criterion for irreducibility…

A: see below the answer with explanation

Q: Let f (x) = x4 − 7x3 + 6x2 − 4x + 1. The coefficient of x8 in the 8th Taylor polynomial p8 is

A: Application of derivative

Q: Find (a) ATA and (b) AAT. Show that each of these products is symmetric.

A:

Q: Q3. Show that p = 1– x + 3x? and q = 9x + 3x? product in are orthogonal with respect to the inner…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: Find the values of w, x, y and z in fraction form using (a)Gauss Elimination, (b)Gauss-Jordan…

A: NOTE: According to guideline answer of first question or first method can be given, for other please…

Q: Find the minimal polynomial of 2^(1/3) + i over Q.

A:

Q: Let A,X EM, (C) such that A is positive semidefinit and AX = XA Show that A¹/2X = XA¹/2.

A: Introduction: Definite matrix is significant in studying quadratic forms. Also, in Lyapunov…

Q: b) For 7 in R", we say that is in the kernel of T if T(x) = 0. If x₁ and 2 are both in the kernel of…

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Q: polynomial in V2+i and compute the conjugates of i over Express i as a Q(/2 + i).

A: As per the question we have to express i as a polynomial in (√2 + i) and then compute its conjugate…

Q: Find the Taylor polynomials p3 and p4 centered at a = 0 for ƒ(x) = (1 + x)-3.

A: Given that: The function f (x) = ( 1+x) - 3 .

Q: 13 1 0 Find a mat rix P such that 0 2 0 2

A: Find matrix P such that P-11302P=1002

Q: consider the function y=ax2+bx+c, where a is in the set {n∈ℕ|15}, b is an integer less than 10, and…

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Q: 1 2 Find a mat rixP such that P-1 1 0 0-1

A: TO FIND A MATRIX 'P'   CONCEPT P-1A P= DIAGONAL MATRIX 1 . BY CHARACTERISTIC EQUATION FIND EIGEN…

Q: ALMN has vertices L(-2, 2). M(2, 3) and N(2, 0) L.

A: Coordinates of L = (-2,4) Coordinates of M = (6,-2) In right angle triangle circumcentre is the mid…

Q: Q2) Determine whether the given polynomials form an orthonormal set, and if not, use Gram-Schmidt…

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Q: Find the standard basis B, of Eg for the polynomial q(s) = s + 4s2 – 3s – 18.

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Q: Let z = (2 – 2i) (3 +3/3i). Compute z100.

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Q: Q3) Use the inner product = a,bo + a,b1 + azb2 to find , llp||, d (p, q), and then find the angle…

A: Given: Inner product: p, q=a0b0+a1b1+a2b2 and the polynomials  p(x)=1-x+x2 and q(x)=x-3x2. To find:…

Q: Show that Z[√−D] is not a unique factorization domain, where D is squarefree and positive

A: Given: To be prove Z-D is not unique factorization domain.

Q: Find minima, bmakima and Sndtle points for the funetions fxy)=4x xy+ 5y - 2. x +2by 6x2-2x3+3y+6xy 2…

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Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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