(9) Prove that for integers x, y and z, if x² + y² = z² then either x or y is even.

Q: Let f: [0.2] [5,6] be a function. (a) If the restrictions of f to [0, 1] and to [1,2] are injective…

A: Solution

Q: Show that a a¹ = 1 (mod p) ()-(-)

A: We use the congruence property of Legendre Symbols to answer this question. We shall show that if…

Q: The sum of infinite number of terms in G.P. is 20 and the sum of their squares is 100. Then find…

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Q: (CLO3) Find a recurrence relation and give initial conditions for the number of bit strings of…

A: To find: We have to find a recurrence relation and give initial conditions for the number of bit…

Q: COS b) MTX -L The functions sin orthogonal set on -L≤x≤L, then show (MIX) cos (nIX) L COS L for m=…

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Q: firm is expected to pay a $2 dividend in year 1, a $3 dividend in year 2, a $4 dividend in year 3,…

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Q: etermine the average value of f(x) over the interval from x = a to x=b, where f(x) = a=4 14 and b=…

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Q: 5. The series is n=0 (sin 2) 3n 10n (a) A convergent p series. (b) A divergent p series. (c) A…

A: Given series is  an=∑n=1∞sin(2)3n10nwe have to check if this series is convergent and also type of…

Q: Consider the vectors in = V₁² 5 -1 1 V₂ = 2 Write the system, which corresponds to the equation a₁v₁…

A: We will solve both questions. The questions are related to vector space. Let's solve

Q: b. For what values of x does f(x) have a relative maximum? Explain. C. Determine the open intervals…

A: Given graph

Q: Q3: Generate the surface having four sides with parameters u and v: [ X = 3u+v, Y = 5v+u], Then…

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Q: Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric.

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Q: Please write this out on paper, I cannot really understand this typed format!

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Q: Problem 1: Diagonalize A and compute SAKS-¹ to prove this formula for Ak: A A = 1 [54] 04 has Ak * =…

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Q: Find a basis for the following subset of P2: { p(t): p'(1) = p(2) }

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Q: In bucolic farm there a contagion spreading among 500 happy cows, some with spots others with- out.…

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Q: A² A³ - + 2! 3! Ife is defined as e¹=1+A+ X - 1⁰ *].0<x< Xx the functions f(x) and g(x). where A =…

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Q: Find the missing coordinates such that the three vectors form an orthonormal basis for IR³ : 0.8…

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Q: dependent: --8--8---8---8 V3 = VI 1 0 V2 = 2 V4= 3 4 Solve c₁v₁ + c₂2+ C3V3+ C4V4 = 0 or Ax = 0. The…

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Q: If S= √√√3-1 2√2 √√3+1] 2√2 √√√3-1 2√2 A √√3+1 2√2 P = S (adj.A) ST, then find matrix ST p¹0 S. and

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Q: ind the equations of the bisectors of the angles between e planes 2x −3+2+3-0 und 3x - 2y +62 +8-0…

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Q: Ife is defined as e¹=I+A+ where A = *].0<** the functions f(x) and g(x). 4 + 4 + 4 + -1 [1(x) 8(x)]…

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Q: --------- = = 2 be three 3 Let U₁ = 2 3 vectors in R 0 a) Show that these vectors are linearly…

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Q: 3. Use Lagrange multipliers to solve for the dimensions of a closed right circular cylindrical can…

A: Let the height and radius of can be h and r. So, the volume of the can is π r2 h V = 2 π  in3π r2h =…

Q: - [a C b If A = where a, b, c and d are real numbers, then prove that A²-(a + d)A + (ad-bc) I=O.…

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Q: 8. Let T: R² R³ be given by T(x, y) = (x+y, x-y, 2x + 3y). (a) Find the matrix of T with respect to…

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Q: Write the equation of the line perpendicular to 2x - 3y = 7 and passes through (2, 1). 2X

A: To find the equation of the line perpendicular to 2x - 3y = 7 and passes through point (2,1).

Q: If A and B are square matrices of the same order such that BA, then prove by induction that AB" =…

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Q: y' = y²(1 + 2x), y(−1) = 1, dx = 0.5

A: Given: It is given that y'=y21+2x. Also, y-1=1 and dx=0.5 .

Q: P = If possible, find an invertible matrix P so that D = P-¹AP is a diagonal matrix. If it is not…

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Q: The polar equation rsin²0 -∞ < t < ∞ represent exactly the same curve. = 2 cos 0, 0 <0 ≤ /2 and the…

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Q: 25. Use Renyi's theorem to prove that if {Xn, n ≥ 1} is iid with common con- tinuous distribution n…

A: Renyi's theorem states that if a sequence of random variables {X_n} is independently and…

Q: and the equation of the bised of the angles between the plan 22- -J+²2+ ³ 32 - 2y +63 + 8 -

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Q: Transform the given system of differential equations into an equivalent system of first-order…

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Q: metic progression whose common difference is nonzero, the sum. qual to the sum of next n terms.…

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Q: B (60, 100, -30) mm

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Q: If the A.M. and G.M. between two numbers are in the ratio mn, then prove that the numbers are in the…

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Q: Question Select one: O True O False ): The set V Give your reasons - {[i]; GER} is a subspace of the…

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Q: Use the Laplace transform to solve the given initial-boundary-value problems. U₁ = Uxx, u(0,1)= 0,…

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Q: (13) Let 2 * - ( 1 ) --- ()) + - (1) = = = 0 Show that Span (V1, V2, 3) = = ܕܐܐ ܕ Span(1, 2) and…

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Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

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Q: 1) The dimension of the subspace of P3 consisting of all vectors of the form at³+bt2 + ct+d, where b…

A: We have to find the dimension of the subspace of P3 which consists the vector at3+bt2+ct+d   where…

Q: Problem 4: Reduce A to U and find det(A) = product of the pivots: 1 1 1 -(0) 121 123 A = A= 113 223…

A: REDUCE A INTO UPPER TRIANGULAR MATRIX OR ECHLEON FORM ,

Q: Copy of Evaluate: [2] = [√5] = [-3] = [-2.1] = For Blank 4

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Q: 2. Let A = [1,3], B = {5}, and C = [4,6]. Write the inequalities (or equalities) that specify each…

A: As per the question we are given the following sets : A = [1, 3] , B = {5} , C = [4, 6] Now we have…

Q: or each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

A: p-series Test : A series of the form ∑n=1∞1np is called p-series, its convergent when 0&lt;p&lt;1…

Q: (D² − 1)y=e*(x² + 1)

A: THE HOMOGENOUS EQUATION IS , D2-1y=0 SO, THE AUXILLARY EQUATION IS, D2-1=0⇒D=1,-1 THE HOMOGENOUS…

Q: Show that the solution of the equation -B [1- 1-* Έναβ J where a, ß are arbitrary. Αναβ α X Z = 0 is

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Q: -4 7 3 -56 Given v = 3 3 a -10 ܠ ' -6 find the closest point to in the subspace W spanned by -6 and

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Q: ) Let A = -3 4 0 1 0 -3 -3 0 3 have eigenvalues A₁, A2, A3. We know that v = (3 0-4) is an…

A: As per the question we are given a 3×3 matrix A and its eigenvalues are denoted as λ1 , λ2 , λ3 from…