Recent content by smerhej

Homework Statement We have y'' + 4y' + 4y = 0 ; find the general solution. Homework Equations Reduction of Order. The Attempt at a Solution So when determining the roots of the characteristic equation, -2 was a double root, and therefore we can't simply have c1e-2t + c2e-2t. So I thought...

Ok so I'm pretty sure I got the derivative worked out. First we're trying to figure out d(f o g)/dxdy. So differentiate with respect to y first then x. Doing so gives: [ df/dy = 4y3 df/du + xdf/dv ] Differentiating with respect to x gives: [ 4y3d/dx(df/du) + df/dv +d/dx(df/dv) ]...

Homework Statement Let f(u,v) be an infinitely differentiable function of two variables, and let g(x,y) = (x^2 + y^4, xy). If f_{v} (5,2) = 1, f_{uu} (5,2) = 2, f_{vv} (5,2) = -2 and f_{uv} (5,2) = 1, computer d^2(f o g)/dxdy at (2,1)Homework Equations The Chain Rule The Attempt at a...

What we know is a is an element of some field F, and the dot is multiplication. What I wrote as the problem is the entire question.

Homework Statement Establish a \bullet 0 = 0 Homework Equations A few axioms I thought to be relevant.. The Attempt at a Solution a = a a \bullet 0 = 0 \bullet a (a \bullet 0) - (0 \bullet a) = 0 a(1 \bullet 0) - a(0 \bullet 1) = 0 a[(1 \bullet 0) - (0 \bullet 1)] =...

Homework Statement Well it isn't so much the problem as it is the notation used within the problem. But here is the question: [SIZE="4"]Determine whether or not \overline{w} and \overline{v} are linearly independent in R4/U Homework Equations [SIZE="4"]If v \in V then \overline{v} =...

Also in case the notation is different elsewhere, lambda = eigenvalue.

Homework Statement Let A = \begin{bmatrix} \lambda & a \\ 0 & \lambda \\ \end{bmatrix} and B = \begin{bmatrix} \lambda & b \\ 0 & \lambda \\ \end{bmatrix} Assuming that a ≠ 0, and b ≠ 0 ; find a matrix X such that X-1AX = B. Homework Equations (A- \lambdaI)v=0...

The original matrix A! Thank you! I don't know how I didn't think of that to check my work..

Homework Statement Let A be the matrix: -5 -3 18 10 Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A. Homework Equations DetA - xI (A-\lambdaI)v = 0 The Attempt at a Solution So, I found DetA- xI, which...

Yes, very much so. :\

I can't tell if you just insulted me or told me that I finally arrived at the appropriate answer.. Either way thanks for all your help (everyone)!

Alright, so let me try again. |v-w|2 = |v|2 + |w|2 - 2|v||w|cosθ so, 2|v||w|cosθ = |v|2 + |w|2 - |v-w|2 " " = |v|2 + |w|2 - (|v|2 + |w|2 -2(v)(w)) " " = 2(v)(w) |v||w|cosθ = (v)(w) Yes? But is that saying that the dot product between v and w is...

Hold on.. If 0 = 2 |v| |w| cos (theta) then that means cos of theta has to equal 0 (so cos of 2 over pi) meaning the angle is 90 degrees, meaning the two vectors are perpendicular. Right?

Right sorry, So doing the dot product of the LHS gives us: |v|2 + |w|2 Then, we substract the lengths |v|2 + |w|2 of the RHS from the lengths |v|2 + |w|2 of the LHS , which leaves 0 = 2 |v| |w| cosθ I'm still confused as to where this is going. I really am sorry for being so...