Find an orthonormal basis of the plane x1+ 5x2 – x3 = 0. }

Q: а?у" - Згу' + 4у %3D 0, у(1) — 5, у'(1) — 3. || ||

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Q: 9. x, - 2x, = -1 2x, + x, = 3 = -7 10. -x, + 4x, = 1 3x, - 2x, = 2 12. x, + 3x, - x = 5 = 5 Xz + 2x3…

A: We have to find the approximate solution using the Gauss-Seidel method.

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Q: 2 If B→ exp exp ( r* – 2), what is V→XB→? %3D

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Q: Find V x (V x F) if F(r, y, z) = 8xyj+ 2xyz k. CS Scannec with CamScanner

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Q: Determine the supremum of the following set with full justification, if it exists. п — Sn = {an | n…

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Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

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Q: 3. (D5 –Dª – 2D³ +18D² –31D+15)y =0

A: Given differential equation is D5-D4-2D3+18D2-31D+15y = 0

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Q: 2x + ys 20 X+ y< 20 x 2 0 y 2 0 Profit : 5x + 6y What is the value of y that gives the best profit?

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Q: in (nx) be a sequence of functions. Show that the series sin Problem 2 Let fn(x) = n2 sin (nx) E fa…

A: Given :  The given series is ;   ∑n=1∞fn(x) = ∑n=1∞sinnxn2 To prove :  We have to prove that the…

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t'i+ t°j K(t)

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Q: Solve the De as follows via Laplace transformations: y"- (14/3)y"- (55/3)y' + 14y 0; y(0) = -1,…

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Q: Solve the initial value problem dy 3. 2t y = 2t°e", y(1) 0. dt Then calculate the value of y(2.7).

A: Given initial value problem is: dydt−3ty=2t3e2t, y1=0

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Q: A company is seiling a new machine. The reliability engineer, has designed the machine to have a…

A: Solution :-

Q: 8. A lamina occupies the top half of the disk x +y? < 4. The density at any point on the lamina is…

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Q: 5. For the function f : Z18 Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s…

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Q: Find the roots of the follo 1 flo)

A: 3. Given the polynomial equation is                                   x3+3x2−6x−8=0

Q: cV9-x2 5) Use cylindrical coordinates to evaluate , L r9-x²-y2 x²dzdydx.

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Q: Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the…

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Q: For the function S : Z4s → Za defined as f(z) = 4r + 1 mod 6. Co defined as zRy when f(x) = f(w).…

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Q: Consider the real sequence {an} given by an = In(n + 1) – In(n+ 2), ne Z>0 = NU {0}. Justify whether…

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Q: a2y" - 5ary/ + 8y= &z$, y(글) =D 0, y'(글) = 0.

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Q: For the given constraints 3x + 8y 0 Profit : 2x + 9y What is the maximum profit?

A: We have to find the best profit .

Q: Let a and o denote two sides of a triangle and let e denote the included angle. Suppose that a, 6,…

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

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Q: |1 0 2 2 1 0 Find the singular values of the matrix A

A: Given matrix: A=102210To find; Singular values of the matrix A.

Q: 8. 3. (1 – cos wt) where w is a positive constant

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A: Note: 80% acid solution means there is 80 ml acid out of 100 ml of the solution.

Q: Find the volume of the indicated region. the region bounded by the cylinder x2 + y2 = 49 and the…

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Q: II. Solve each of the given LDE of order n. 2. y/®) –4y5) +3y/) =-27

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Q: L. If f(x) = J dt, (1 + sin(tº )]dt , find f'(#)- dt, where g(x) =

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Q: A cube of side 2 cm is to be made. However, due to erroneous measurement, the actual side of the…

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Q: y = 3x - x² and y = 2x

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Q: Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the…

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Q: Let T be a linear transformation from M, , such that M2,2 into 1 0 1 -1 0 1 0 2 0 0 1 2 0 0 -1 = 3 1…

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Q: 5. Let A and B be n-by-n matrices. Each of the following statements is equivalent to two of the…

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Q: show Hat the (Rang) ra bounded Linear operater Ti x-oy need not be closed in y. Hint useTe e Yang…

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Q: Find curl (2z i + 3x j+ 2y k). curl (2z i + 3x j+ 2y k) = )i + ( i )j + ( i i )k

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Q: 3x, - 2x, = 2 12. X, + 3x, - X3 = 5 3x, = 5 X2 + 2x3 = 1 ether the matrix is strictly diago-

A: We can solve this using gauss seidel method and strictly diagonally dominant matrix,

Q: Find the inverse Laplace transform of F(s) s2 + 2s – 3 . (Use step(t-c) for u.(t) .)

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Q: b. a. d. c.

A: Solution: