Find solutions of the linear PDE u, + yu, =0 , given that u(0, y)= y'. ди(х, у) ди(х, у) Notation is standard: U = u(x, y); u̟ := ôx ;u, := ây

Q: What are the coordinates of P(23t/2)? А. (-1, 0) В. (1, 0) С. (0,1) D.(0,-1)

A: Solution

Q: If vector A = [4/1] and vector B = [-3/2] find A-B

A: Here two vectors A and B are given we have to find A-B.

Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: Suppose that x 1 4 + y 1 4 = 2. What is y 00 at the point (1, 1)?

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Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: Use the equations to find əz Әх əz ду II - - əz Әх az Әх and =1 . OF Әх OF az and дz ду 5yz + 3x…

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Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: a. A: = a: b: -1 1 1 0 A A This is the result of the inverses of the matrices: 3/2- -1/4 -3/2 5/4 0…

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Q: Determine if u = (4,3) and v = (1/2 , - 2/3) are orthogonal, parallel or neither.

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Q: Suppose u = (-3,0,0) and v = (-3,-2,3). Then: u +0= u – T= | 3u= 7u – 30=

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Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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Q: By using siMPSon method find Sinx da for 3(0,25)

A: Given integral is, ∫01sinxxdx With the step value of 0.25. By substituting the step length the value…

Q: Let u=<-1,1> v=<-3,4> and w=<0,-2> Find u-v+4w

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Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: Express the following as a linear combination of u (2, 1, 5), v (1,-1, 4) and w = (6, 8, 6). (9, 14,…

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Q: If A = ( - 1, 2) and B = (3, 4), find AB and redraw it (a) in standard position and(b) with its tail…

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Q: if given the equation yi = B0 + B1xi +ui and express the same equation as y = xiB = ui (where xi and…

A: Equation :

Q: Express the following as a linear combination of u=(2, 1, 3), v= (1, -1, 4) and w=(2, 8, 8). (5, 14,…

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Q: Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.