Find the QR-factorization of the matrix 2 1 A = 1. -1 -1 121 2

Q: Y(s) U(s) 100 s2+5s+100

A: To transform the following system YsUs=100s2+5s+100  

Q: fhe coefpicient an fiderivative what? rin (2x ) in the fre of of F (A CoS is ン

A: We have to find the coefficient of sin 2x for given problem.

Q: Solve the linear programming roblem using the simplex Maximize P= -x, + 2x2 subject to - x1 + X2 s2 ...

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Q: sov? (2² – 2) (2a² – ²) } æ²)

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Q: Calculate whether it is convergent or divergent. (4x)2* x=1

A: Given series is ∑x=1∞(4x)2xexx2x

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: Proof by Contradiction Provide a proof by contradiction of the statement below. For all integers x, ...

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Q: . Show that x2 + 3 and x2 + x + 1 over Q have same splitting field.

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Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the percent...

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Q: Show that Foranyeigen value Tofthe nonsingu lar matrix A with any natural norm Then

A: Given, Eigenvalue λ of non singular matrix A To prove : 1∥A-1∥≤λ≤∥A∥

Q: 3. Let f(1) = r and for each real number n > 1, define the function In (x) = 1 – 1– |z| (i) Find the...

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Q: 1. Find the general solution of the given differential equation using MUC: y(4) – 4y(3) – 21y(2) + 1...

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Q: ind the moment with respect to x = 2a the area bounded by x = 2y and x2 4ay.

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Q: sider the curve C defined by the equations x = t° + 3t? and y = 2t + 15t2 + 36t + 6. Show that C is ...

A: We have to show that Given curve is smooth.

Q: Q7

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Q: 4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the...

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Q: Advanced Math Question

A: As it is given that A is a skew-symmetric matrix, it can be concluded that AT=-A.

Q: Compute the determinant using a cofactor expansion across the first row. Also compute the determinan...

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Q: min 4a1 + 5xз subject to 2x1 + x2 – 5x3 -3x1 = 1 + 40з + х4 — 2 x; > 0, i = 1, 2, 3, 4.

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Q: y' + 4y = cos(t);y(0) = 0 = CO

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: 9. Test the following for convergence (p and q denote fixed real numbers): (a) Σ1P"n"; p > 0

A: Please specify which subpart is to be solved. Here is the solutions of subparts. (i) The given serie...

Q: Given the vector function: 7(t) = (e', e' sin(t), e cos (t)) Determine the equations of the normal p...

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Q: Given the vector function 7(t) = (t +3, 7t – 5) %3D Calculates the principal normal vector (t)when t...

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Q: (x+ 7)" Σ 2n Vn2 – 1 n=2

A: This is a problem of series.

Q: Find the area of the region bounded by y = -x² – 4x – 2 and y = 2x2 + 8x + 7.

A: Area bounded by curves

Q: Use sigma notation to write the Taylor series about x = 9 for the function. 1 x + 5 Σ k

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Q: 1. Consider the following graph: e6 U5 e3 U3 (a) Write the vertex set and the edge set, and give a t...

A: The given graph :  

Q: Given system of linear equations: х+у—3z %3 4 2х + 4у — 4z %3D 5 —х + у + 4z %3D —3

A: Solve using Cramer's Rule. Show complete solutions.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: a The population of Kenya was 30.7 million in the year 2000 and 38.3 million in 2010. a) Find the gr...

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Q: Suppose you are cooling a hot extract in a 24°C process room. The temperature of the extract right w...

A: 66.9 deg.C

Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,...

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Q: min -5x1 –- x2 + 12x3 subject to 3x1 + 2x2 + x3 = 10 5x1 + 3x2 + +x4 16 X; > 0, i = 1, 2, 3, 4. for ...

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Q: P= 28x1 + 12x2 (A) Using slack variables, determine the initial system for the linear programming pr...

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Q: -3 -3 1 2. Let C = 6. and B = -6 -6 -3 4 7 A. Find PC→B. -5 B. Let u = 8 Find [u]c. -5 C. Use part (...

A: As this problem is related to change of basis of a matrix, hope you know how to find inverse of a ma...

Q: Determine the surface area generated when a portion of the curve in the first quadrant of y² = 4 +x2...

A: We will find the surface area generated by a given curve in the first quadrant

Q: Evaluate the following: 1. "(1 – x)e-*dx -∞ exdx 2. S - 00 1+e2x dx 3. J1 x(x+4)

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Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and ...

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Q: A cylindrical tank of radius 5 ft and h.

A: Given, a cylindrical tank of radius 5 ft and height 6 ft is two-thirds filledwith water.

Q: find eigenvalue/eigenvalues and the corresponding eigenvector/eigenvectors of A. 1 -1 1 A = -2 1

A: As you mentioned to do just part (a), the answer of part(a) is given in the following steps....

Q: 1$ A and B are positive semide are Lal allnegative all non negatie El gllpositve y noneofabove

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Q: Find the area bounded by the parabolas (x – 1)² = 4ay and y² + 4a = 4ax.

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Q: 4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the...

A: Given Newton's law of cooling says that the temperature of a body changes at a rate proportional to ...

Q: (b) Let n > 2 and let x1, x2, . .. , Xn+1 E R with x¡ # x1 for all 2 - Define the (n+ 1) × (n +1) ma...

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Q: Find the moment with respect to x = 2a the area bounded by x = 2y and x2 = 4ay.

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Q: .Find the solution of the given initial value problem using MVP: 4y(2) – 8y(1) – 5y = x3e2x – 8x y(0...

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Q: -3x1 + x2 + 12x3 = 50 6x1 – x2 – x3 = 3 6x1 + 9x2 + x3 = 40

A: Here we consider X1=x,  X2=y, X3=z (for Easier to solve) .  So, 

Q: 3. How many integer solutions are there to the equa- tion X1 + x2 + x3 = 9, with x; > 0? How many so...

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Q: 5. Show that there is no vector field G such that: V x G = 2xi + 3yzj – xz?k.

A: Given that ∇×G→=2xi^+3yzj^−xz2k^. We have to show that there is no vector field G→ such that ∇×G→=2x...

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs o...

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