Let A = -- 1 1 2 5 1 -4 4 -4 7 2 1 2 3 -3 and y = 4 1 Find an orthonormal basis of Col(A). Find the distance of y to Col(A).

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Q: = 3. Let fn be the nth Fibonacci number (so fo = 0, f₁ = 1, and fn fn-1 + fn-2 for n ≥ 2). Find…

A: Let fn be the n-th Fibonacci number where f0=0, f1=1 and fn=fn-1+fn-2 for n≥2. To find an upper and…

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A: we know that      a-b ≤a-b

Q: 2. find u (x, t) for 0 0 which solves Ut - Uxx = e¹, u (x,0) = 1, u (1, t) = u (0, t) = 0.

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Q: Give either an example of a function from R to R for which f(A)=B, for A and B open sets in R (open…

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Q: 8. 2(w+1) 2 - 4 2w+22-4 212-4-2 212-6 ما wZ I JIN w 2 -3 9. 3(n-3) ≤ 18 34-9≤18 3n≤18+9 34527 n≤ 27…

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Q: Q9. Consider the following algorithm: sum = 0 For j starting at 1 and ending with 15: sum = sum +…

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Q: Let

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Q: Estimate the instantaneous rate of change of the function f(x) = x³ + 3x² − 4 at x = 6. c. -144 d.…

A: Solution :  Given  f ( x ) = x3 + 3x2 - 4   .......  ( 1 )  We know that the rate of change of the…

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Q: Find the matrix exponential The eigenvalues of A are X₁ = -1 and ₂ = 1. In the event that your…

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Q: Problem 8.3 Vector fields Sketch (qualitatively) the following vector fields for -1 ≤ x ≤ 1 and -1 ≤…

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A: Given:Graph  To check that graph have an Euler path.

Q: Find an orthogonal basis for the column space of 6 -4 2 6 1 0 0 1 0-2 -2 0

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Q: Determine £¹{F}. sF(s)-F(s) = s+3 s² +2s+1 2 Click here to view the table of Laplace transforms.…

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Q: 9. Find the volume of the solid generated by revolving about the axis y = 8 of the area bounded by…

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Q: 4.4.14. Find a basis for the orthogonal complement of the following subspaces of R4: (a) the set of…

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Q: 1. In the graph, indicate which point is the image of P under: Example: The reflection with line 1₁…

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Q: h(t) 1-cos 2t t

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Q: Calculate (5xy + 4e²) dS, where S is the triangle with vertices (0, 0, 3), (1, 0, 2), and (0, 4, 1).…

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Q: 8. Solve for x (ABCxEFG)2 = T². Your solutions should be expressed in terms of absolute values of A,…

A: Solution : 2 Given        (ABCxEFG)2  = T2        .......... ( 1 )  Form equation (1)     A2 . B2 .…

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Q: Problem 4. 1. For n = 3, explain why Lo(x) + L₁(x) + L₂(x) + L3(x) = 1 for all x, where Lo, L1, L2,…

A: To Explain : 1) For  n=3 why L0x+L1x+L2x+L3x+L4x=1 for all x where L0 , L1 , L2 , L3 are the…

Q: 3. Let ƒ : A → B be a function. Prove that if ƒ has an inverse, then fis bijective.

A: This question is related to topic function from real analysis.

Q: Prove that the equation x4-y4 = z² has no integer solutions.

A: Note: We will be solving part (b) as mentioned. The given equation is x4-y4=z2. Observe that…