For which value of a the system of ODES —D У1 + ау2 + (е -У — 1), У2 3D —ауј — У2 has an unstable focus at (y1, y2) = (0,0)

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: V (b) u. u (c)…

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Q: -65 -140 30 65 a. If possible, complete the following equations; otherwise, enter DNE. °][³]= [2]…

A: Note that : Since you have posted a question with multiple subparts, we will provide the solution…

Q: Given the rule (x,y) --> (x-4, y+8), describe what transformation occurs to any given point

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Q: 7. (а) X1 3x2 = 1 2x1 - 6х, — 2 | %3D

A: The solution is given as

Q: 5. Compute the distance between these pairs of points: (a) (-2, 5) and (4, 13) (b) (3,-4) and (8, 8)

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Q: - a +b -c+d = 0 - 2a +b+c-3d = 0 b) a+ 2b – 3c +d = 0 2a +3b +4c– d = 0

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Q: Find an equation of the line that passes through points P(2,-3) and Q(5,-1).

A: The equation of the line that passes through points x1, y1 and x2, y2 is given by…

Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: 2) g(x)= -2 () 2x+1 Transformations: a= b= h= k=

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: The independent variable(s) of the equation Urr B- uy + aug is/are ох, у a, ß о и, х, у

A: The given differential equation is:uxx=β2uy+αux

Q: Find (5x + 3y)dA where R is the parallelogram with vertices (0,0), (-1,4), (-4,-5), and (-5,-1). R…

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Q: Find u - v, 2(u + 3v), and 2v - u. u = (6, -2, 4, 3), (-2, -1) (a) u - v = (b) 2(u + 3v) = (c) 2v -…

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Q: Find u v, 2(u + 3v), and 2v- u. - u = (6, -5, 8, 3), (a) u-v= (b) 2(u +3v) = (c) 2v - u = v = (-2, 5…

A: The solution is shown below-

Q: Find the Jacobian of the transformation = 2u+7v, y u² - 5v. =

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Q: valuate a.j8 1 b.- ¡7

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: The standard form of the equation of a line going through (3, -3) and (0, 2) is: 5x - 3y + 6 = 0 Oy…

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Q: Find the Jacobian of the transformation x - 3u + 7v, y = u² – - v.

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Q: Suppose the solution set of a certain system of linear equations can be described as x₁ = 5+ 3x3, x₂…

A: Given,The solution set of a certain system of linear equations can be described as with  free. Aim:…

Q: Each of J, K, L, M and N is a linear transformation from R? to R². These functions are given as…

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Q: 9) Find the equation for the line in space passing through the point (-2,2,-2) and parallel to the…

A: Let two points are so equation of line passing through above two points is given as follows

Q: What are the coordinates of latera recta of the equation 16x² + 9y² + 64x – 18y-71= 0? 17 17 ,1+. 1…

A: Given query is to find the coordinates or latera recta of the equation.

Q: Let u = [-1, 2, 2] and v = [1, -1, 1] Find (급x) O [3, 4, 1] [3, 4, -1] OI-1, 3, 4] O 14, 3, -1)

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Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…