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    Bases and Dimension: Prove the plane P is a subspace of R^3

    I'm on the basis and dimension (vector spaces) chapter of my textbook and need to prove the following: Consider the plane P in R^3 whose equation is x+y+z=0 prove P is a subspace in R^3. I suspect they don't want to us to use the method of proving subspaces by showing closure under...
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    Reduction Formula and factorials: I_mn =int(x^m (1 - x)^n, x=0..1) = m!n!/(m+n+1)!

    Show Imn =int( xm (1 - x)n, x=0..1) = m!n!/(m+n+1)! really having trouble with this one. first thing I tried was just integrating by parts as it is, which I couldn't make work. I tried changing the expression to: Imn = int( (xm-1) (1-x)n (1+x-1), x=0..1) which simplified to: Imn =...
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    PDE chain rule

    Suppose that f is a differentiable function of a single variable and F(x,y) is defined by F (x, y) = f (x2 − y). a) Show that F satisfies the partial differential equation ∂F/∂x + 2x•∂F/∂y = 0 b) Given that F(0,y) = sin y for all y, find a formula for F(x,y). for a) I take LHS...
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    Is the set S a subspace of P_3

    I'm not even sure I'm interpreting this question properly. Q: is the set S a subspace of P3 S = { p element of P3: p'(x) + x + 1 = 0 for all x is an element of R} now, first of all, I'm a bit confused with the vector space of P3 . Is it the space of polynomials of degree 3 or less or do the...
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    Show the set T is a vector subspace of R^3

    Show the set T is a vector subspace of R^3 T = { Sum( µivi , i = 1..4 ): µi is an element of R, 1<= i <= 4 } where v1, v2, v3, v4 are fixed vectors in R^3 the solution so far: so if I expand the summation and call it v v = µ1v1 + µ2v2 + µ3v3 + µ4v4 it is this correct...
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    Show the set S is not a vector space with the usual rules of (x+)

    H i, so I'm working my way through course notes over the uni break and its a new topic and hard for me to clearly understand the notes as I don't have a lecturer going over them yet. So forgive my butchering of this as I'm trying to understand it. Problem: Show that the set S={x element of R^3...
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    simplify (matrices) (A B A^-1)^6

    simplify (A B A^-1)^6 A and B being matrices where AB exists the answer given is = A B^6 A^-1 I'm baffled how to get this answer, any help, please? and one more question, I can't seem to find an answer anywhere online. If you have (AB)^-1 it becomes B^-1 • A^-1 is the same...
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    Prove | z - Re(z) | >= | z - x |

    Prove | z - Re(z) | <= | z - x | for all real numbers x, draw a sketch to illustrate the result. ----------------------------------------------------------------------------------------- really confused on what to do here. Even after seeing the sketched solution I'm not sure how they...
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    a particles location is given by s = 3cos 2ti + 3sin 2tj, confirm its in a circle

    "A particle is moving such that its position is given by: s = 3cos 2ti + 3sin 2tj a) confirm the particle is traveling in a circle." Hey, Ive been really stuck on this problem and Im not really even sure where to get started. My first thoughts were trying to express the equation in some...
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    quick question on limits, undefined or infinity as the answer

    hi im working through my maths lecture notes and i seem to be having a misunderstanding about when a limit is undefined or its infinite. for example: lim x->0 cosec (x) lim x->0 1/sin (x) = 1/0 I would have thought to label this limit as undefined as it shoots of to +- infinity at x=0...
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    Solve sec 2x = 2 between -Pi < x < Pi (can't find all the soln values)

    having trouble finding all the angles. I can get: sec 2x = 2 = cos 2x = 1/2 2x= pi/3 x= pi/6 positive cosine is quadrant (Q) 1 and 4 Q1= pi/6 Q4 = (2pi - pi/6)-2pi = -Pi/6 (adjusted to parameters) theres two more angles however, 5Pi/6 and -5pi/6 which Im not sure how to get. The 2x I'm...
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    Show that .... is independent of theta

    Show that: [(1 + cotø) / cscø] - [(1+tanø) / secø] is independent of ø. The above equals 0. But what does it mean to show that it is independent if ø? is it because no matter the value of ø the equation is always 0? help me understand how to think about this please!
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    point slope form

    in my text book you are given: m= 4/3 and a coordinate (2,-3) then place it into point slope form then solve it as y=mx+b so I had: (y-(-3))= 4/3(x-2) y+3 = 4/3x -8/3 y= 4/3x -8/3-9/3 y= 4/3x - 17/3 but the answer is listed as y= 4x/3+1/3 where am I going wrong? thanks
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    solving for variable: is it possible to solve R^2 +10R = 2000 be R = something?

    is it possible to make this equation: R^2 +10R = 2000 be R = something? i can't figure it out if there is. I was working on a word problem and got the equation down to this trying to find the rate of something. But this is where Im stuck. I do know that the R^2 +10R = 2000 is correct as i...
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    purplemath work word problem

    Im working thru on of the sites work problems here: Im fine all the way up until the end. I feel like Im missing something obvious, but its not clicking for some reason. from the last section "finishing the job:" 20(1/100 + 1/120 + 1/t) = 0.45...
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    Equivalent Expressions: ""The area (in square meters), a, of a yard is given by...."

    Equivalent Expressions: ""The area (in square meters), a, of a yard is given by...." Hi, first post, and probably not my last lol Ive been using Kahn Academy to teach myself maths again from the begining. One of the frustrating things about that site is sometimes they start throwing questions...