* The given matices , verify directly thart (RS)* -5*R* and (E) - p*i* 3 i . R= 3i %3D 1

Q: EXAMPLE NO. 1 Reduce the quadratic form x2+y²-9xy into a canonical form of the matrix.

A: Converting quadratic form to symmetric matrix form.. Here, we have 2 variables in quadratic equation…

Q: 0.03-0.02-2.576/0.03(1-0.03)/300, 1-[ Vo.02(1–0.02)/300

A: Sol

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy dA ax ду for the given path. C:…

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Q: Let М — 2 Find formulas for the entries of M", where n is a positive integer. 2·4" – 3" 2(-4)"+2· 3"…

A: The solution is given as

Q: b). Consider the function f(x.y)=-(x²-1) -(xy-x-1)'. ). Find the critical points of f (x, y).…

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Q: 6. Given vectors spaces V with bases B and E and W with basis D and a linear transformation T:V→ W,…

A: Sol

Q: 5. ints) Let v1,..., Un be vectors in a vector space V. Suppose w is another vector in V. Determine…

A: To prove: :  Span(v1,.....vn)=Span(v1,v2,....,vn,w), if and only if  {v1,v2,......vn,w} is linearly…

Q: If two dice are rolled, find the probability ofshowing a sum of 7 or 11 ? 1/18 7/36 14 2/9

A:

Q: Perform the Gram-Schmidt process on the following sequence of vectors. i = |8, -2 8 -5

A: Given sequence of vectors arex→=488, y→=-4-2-5, z→=1-15The Gram-Schmidt process on the following…

Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

A: Given field : F=x2yi+2y3zj+3zk    surface S is r(r,θ)=(r cosθ)i+(r sinθ)j+rk    0≤r≤1,     0≤θ≤2π

Q: The probability that a marriage will end in divorce within 10 years is 0.25. What are the mean and…

A: Solution :  Given that  The probability that a marriage will end in divorce within 10 years is 0.25.…

Q: L(eT+h) = ae?+h +h = YT+h - ÎT+n/T. Assuming that YT+h~N(µr+h»o%+n}; show that the optimal s equal…

A: Sol

Q: etermine trigonometric coefficient 2 1 2

A: Sol

Q: istance of magnitude directed oPposite to the velocity, 1325 the velocity v is measured in m/s. Use…

A: Sol

Q: 10) ~p V (q ^ r) * True O False

A: 10) Truth table is given by p q r (¬p ∨ (q ∧ r)) F F F T F F T T F T F T F T T T T F F…

Q: 3. 2х, — х, = 2 X - 3x, + xz = -2 3x3 —х, + х, — 3х, — —6 -X, + x2

A:

Q: Given the graph of the following data points: 10 12 A = (1, -2) -2 B = (3, -3) C = (5, -4) D = (8,…

A: Statistics is a branch of mathematics that gives us the tools to deal with large quantities of data…

Q: Let S be the equivalence relation on {− 1, 0, 1} × {0, 1, 2, 3} defined by (a, b )S(c, d) if and…

A: Let A  = {-1,0,1}×{0,1,2,3}  i.e A=…

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

A:

Q: EXAMPLE NO. 2 Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Converting quadratic form to symmetric matrix form. Here, we have 2 variables in a quadratic…

Q: Write an equation for the function graphed below. Use the smallest powers possible to meet the…

A:

Q: Write the statement in words if: p: Firemen work hard. q: Firemen wear red suspenders 4) ~(q ⋁ p)

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Q: You are transferring to a new house. You have a collection of books but you cannot take them all…

A: We want to find true option.

Q: Let -5 1 0.5 4 –2 -1 -17] Use the Gram-Schmidt process to determine an orthonormal basis for the…

A:

Q: 12. Consider the very accurate map below. We want to color these six countries so that no two…

A: Solution: a) Using 3 colours it is not possible. First thing we shall observe that a single color…

Q: Euler Paths and Circuits Use the theorems for Euler paths and circuits to determine if the graphs…

A: The Euler paths or circuits of the given graphs are determined by using theorems as shown below.…

Q: Find an orthonormal basis of the plane r1+ 6x2 – 23 = 0.

A: Solution

Q: r1.5 4. Use a suitable numerical method to estimate (xsin (x²) + 4)dx using 10 ordinates. Use at…

A: Given integral is∫01.5xsinx2+4dxThe integral is solved using midpoint rule using 10 ordinatesas…

Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: Write the statement in words if: p: Firemen work hard. q: Firemen wear red suspenders. 4) ~(q ⋁ p)…

A: We have to write the statement in words.

Q: Find the eigenvalues A1 < Ag and associated orthonormal eigenvectors of the symmetric matrix -5 -5 3…

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Q: dx2 dx 4. Evaluate L(sint - cost)?.

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Q: For each set of three points, there is exactly one line containing them. If a point is not on a…

A: Please find the answer in next step

Q: -3 Given v = 9 10 find the coordinates for v in the subspace W spanned by 2 1 4 u1 = 2 U2 = and uz…

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Q: 2y+y = x²e 3x. d?y thod - dx2 2. Solve by method of variation of parameter - 2 = ex sin x. %3D dx?…

A: Solution by a variation parameter method

Q: Find the following expressions if a = 3i – 5k, b =i+j-5k, and c = 4i + 9j + 3k. 1. a · b = 2. а : с…

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Q: the following: ve that for all k EN and x > 0, g(k)(x) = PkC e-1/x, for some polynomials på 9k(x)…

A: Sol

Q: Exercise 94. Evaluate ſcF dr where F(x,y)= xi- yj and C is the line r(t) = (1 -1, t), 0<I<1. If a…

A: Vector field and conservative vector field

Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(x)

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Q: - 2 0 6) Graph the transformation of the unit square using Tx) = Ax and A 3 4

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Q: Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Given quadratic form 3x2+5y2+3z2-2yz+2zx-2xy.

Q: be a collection of sets in S'. Show that we can express U E, as the disjoint union U, Er of sets in…

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Q: The frog population in a small pond grows exponentially. The current population is 95 frogs, and the…

A:

Q: 1.36 (a) Show that any set of four vectors in R2 is linearly dependent. (b) Is this true for any set…

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Q: 1. Solve by D operator method dx2 d?y 20 +y = x²e3x dy dx

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Q: Use the Laplace transform to solve the given initial-value problem. у" + 2y" - у' - 2у %3 sin(3t),…

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Q: higher productivity Eg G Good patch a lower productivity Average patch n Poor patch Travel time…

A: Sol

Q: alespeople for a solar technology company have average annual sales of $200,000, with a standard…

A: Statistics is a branch of mathematics that gives us the tools to deal with large quantities of data…

Q: A triangle is inscribed in a parabola such that the first vertex (point A) is at the origin and the…

A: Given that,A triangle is inscribed in a parabola such that the first vertex (point A) is at the…

Q: 1. Solve by D operator method d?y dy -2y +y x2e3% dx2 dx Solvo hu

A: