Q1) Evaluate the integral dy dx using polar coordinate

Q: Question 23 Let H dimH? Span{1+x, 1+a, 2 + a + x2, 3 + 2x + a}. What is

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Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R“, where bị b2 3 3] C1 3 C2 22 a If the…

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Q: Question 26 1 2 41 a Let A = -1 1 -1 6 is in NulA, If 1 1 3 then the value of a is and the value of…

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Q: Question 34. Let A be a symmetric matrix. Suppose that u and v are two eigenvectors of A…

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: by (E)- HA (). [6 11 If B = is a basis for R such that T|B is a diagonal ma %3D then the value of a…

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Q: Question 18 Let B = {1+x, 1 – x2, x + 2x} and p(a) = 7+ 10x + 11a?. You are given that B is a basis…

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Q: = {b1, b2} be a basis for a vector space V. Let T:V → V be a linear transformation with the property…

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Q: Write TRUE if the statement is always correct and FALSE if otherwise. (a) If an >0 for all n E N,…

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Q: , counting the multiplicities. Then A is orthogonally diagonalizable.

A: We have to examine that matrix A is orthogonally diagonalizable or not.

Q: Let A be a 2 x 2 symmetric matrix satisfying A = 12 and 3 with the spectral decomposition le A = 12…

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Q: Suppose that A is a 14 X 9 matrix that has 6 pivot columns. Then: (1) dim(ColA) is (ii) dim(ColA)+…

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Q: Let S be the solid inside the sphere p = 6cosdand below the cone 0 = 1/4 Set-up the iterated triple…

A: Volume using cartesian coordinates is given by V=∬∫V dzdydxwhere x=ρ sin ϕ cos θy=ρ sin ϕ sin θz=ρ…

Q: c2-x Q1) Evaluate the integral f. S. ** dy dx using polar coordinate

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Q: Question 4 Consider the function (a) State the domain of f(r, v). f(I, v) 3zy (b) Find the limit by…

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Q: Solve for the general and particular solution using Laplace Transform y" +y = sqrt (2) (cos sqrt…

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Q: For all x E R, e* xn n! a. Express f(x) = x?e* as a power series %3D b. Find the third-degree…

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Q: –10° | The eigenvalues of 1 are 3 and

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Q: . Find all the solutions of 3x² + 2x + 1 8 (mod 63).

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Q: (4) Which of the following graphs shows the solution of the initial value problem dy 2x, y = 4 when…

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Q: 2 1 -1 Let W = Span 1 1 . Then, the distance and y = 3 -21 11 from y to W is W is

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Q: Given de - and dy = . Then do and dq are not G- conjugate if G is Non of these 12 O A 0.5 0.25] [18…

A: We want to find matrix for which vectors are G conjugate

Q: aluate L(t(uo - u) +tu,}.

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Q: Question 31 2 1 1 U2 = 1 and W =Span{u1; U2, U3}. For 1 Let Uj = Uz = 1 1. 6. in W ? what value oft…

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Q: What is the minimum number of edges for a spanning tree for this graph?

A: The given problem is related with graph theory. Given a graph. We have to find the minimum number of…

Q: Find the third degree Maclaurin polynomial for f(x) = cot-1(x) and use this to approximate cot-1(1).…

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Q: +00 (5 – 4(ln n)³)" Σ (V3 . In n)3n n=2

A: Given series is ∑n=2+∞(5-4(ln n)3)n33·ln n3n

Q: 1.Does it follow that if an > 0 for all ne N, thenEn=1 an does not converge conditionally? Explain.…

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Q: 4. Find the volume of solid of revolution (in cubic units) when the area of the region bounded by y…

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Q: Let A = ⟨1, 0, 2⟩ and B = ⟨6, −2, 3⟩. Solve for projAB. Then, find the angle between projAB and B

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Q: Q1\calculate x1, x2, xn from the following equations: -3x1 + 9x2 + xn = 2 5x1 - 2x2 + 3x,n = -1 2x1…

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Q: Q.3 An experiment gave the following values : v(ft/min) 350 t(min) It is known that v and t are…

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Q: Consider the function g(t) = e-t (a) Find the Maclaurin series for g(t), stating your answer using…

A: Given: A function g(t)=e-t2. To find: (a) Find the Maclaurin series for g(t), stating your answer…

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Let T : R? → R´be defined by [2 _5||X1 X2 1 6] [x2] а If B = is a basis for R“ such that |T'|B is a…

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Q: An orthogonal matrix is orthogonally diagonalizable. True False

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Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: 3- Vn n=1

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Q: Learning Task I. Use the figure at the right to complete the inequality statements: 1. m21 3. If the…

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Q: Define Euler's P-function. Showing your working, compute (5), D(23) and (115).

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Q: Let A be a symmetric matrix. Suppose that u and V are two eigenvectors of A corresponding to…

A: Given matrix A is symmetric. Its eigenvectors are u and v are distinct. Since we know that, the…

Q: Evaluate the Inverse Laplace Transform 1 F(S)=T51)(s+1)² (s-1) (s+1)²

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Q: Given do = and di = Then de and d, are G- conjugate if Gis %3D Non of these O D [4 21 l2 8l O A B.

A: We want to find the matrix for which the given vectors are G-conjugate

Q: Suppose that x is an eigenvector of a matrix A with corresponding eigenvalue 6. Then x is an…

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Q: Determine whether the following series converges or diverges. If the series converges, determine the…

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Q: Given the matrix G =| 10 5 201 and d, = Then d, and d, are not G- conjugate if d, is given by -1.5]…

A: We know that Two vectors u and v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0…

Q: Question 12 -9 6. The eigenvalues of 1 are 6. and

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Q: +00 1 Find the sum of the following convergent series: n? – 3n + 2 n=3

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Q: Consider the following. W = cos(x - y), x = t², y= 51 (a) Find dw/dt by using the appropriate Chain…

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Q: [3 0 01 Let A 0. 1 3 %3D 0 3 1 Which of the following statements is TRUE about the quadratic form…

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