Ex 8. Let B = [(1,0), (0, 1)) and B' = (v₁, V₂]. Find B' so that (1:1) (1) = x² + 2xy + y² + 10x - 4y +5 can be simplified into f II x² + 2y + 5.

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A: Given series is convergent. Explanation is as follows

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A: As per the guidelines I am answering only first 3 parts. We have  A=12100251103722-211258-18 given…

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A: A trail is an open walk in which no edge is repeated.  Vertex can be repeated.

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A: In your answer this will be 696 place of 632

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A: We need to determine the Laplace transform of the function: f(t)=2tet.

Q: Let u= (1,-1,0,4) and = (1,-1,2,0). Find a vector WE R4 that satisfies - 2 w). 4u wü.v(u =

A: The explanation is as follows

Q: Solve for x E [0, π) 2 cos²x + 3 sin x = 3

A: Sol:- 2cos2x+3sinx=3, 0≤ x&lt;πUse the Pythagorean identity:  cos2x+sin2x=1-1-2sin2x+3sinx=0Let:…