Recent content by Skins

If the plane does not pass through the origin then it is not a vector space (according to definition a vector space must contain the zero vector).

For me LaTeX is the way to go. I tried switching to word processors for a while but very quickly came back to LaTeX for publications both large and small. In general I find formatters such as LaTeX much more flexible and robust. And once you get the hang of LaTeX it just gets easier. There are...

Axler seems to imply that there is definitely a need and a time and place for determinants. However, certain proofs, ideas, and computations can be accomplished in more elegant ways without determinants than with. I tend to agree with this philosophy. However, determinants are by no means...

Okay, fair enough. My bad. I came too close to an actual solution. In retrospect may I rephrase and provide the hint "Consider whether or not the tangent of the angle at P is the same for both triangles and if so what does that imply about the sides of each triangle". In the future I'll take...

One of the beautiful things about Mathematics is that there are often several ways of describing a problem or a solution and they imply the same thing yet each way can be uniquely enlightening, . In this case I am applying the properties of similar triangles just as you suggest, namely the...

I assume you mean Dr. Gilbert Strang ? Where did you see this in Dr. Strang's book ? I can't speak for Friedberg or Axler but, I have reviewed Dr. Strang's lectures and have also read his book which covers determinants in depth and nowhere does he imply that determinants are useless and/or are...

True I should have specified that x must be of correct dimension such that multiplication by A is possible in which x would have to be a square 2x2 matrix in order for the commutative law to be applicable as show above. i.e.if A is a identity matrix then Ax = xA = x iff dimensions of A=...

In order for an arbitrary matrix A to be an identity matrix we must have the condition that for all vectors x Ax = xA = x. The first is clearly a 2x2 identity matrix. the second isn't since Ax neq x

If you write the system of the equations in matrix form and you perform elementary row operations and put the matrix into row reduced echelon form then what is the rank of the matrix ? (Hint...which columns are independent and which are dependent ?) If the rank is r and the number of columns is...

Are you looking for the rate at which the shadow is moving relative to the person or relative to the base of the light pole ?

Think of exactly what the quotient rule states. How would you then apply it to the expression y = (x-a)/(x-b) ?

Hint... for the second limit rationalize by multiplying by \frac{2x + \sqrt{4x^2 + 3x}}{2x + \sqrt{4x^2 + 3x}} So... (2x - \sqrt{4x^2+3x})\frac{2x + \sqrt{4x^2 + 3x}}{2x + \sqrt{4x^2 + 3x}} Then proceed from there with. Factor when possible and simplify radical expressions. Give it a try...

For the first question change the denominator to \sqrt{x^2 - 3} - \frac{x}{2} Then multiply the top and bottom by \sqrt{x^2 - 3} + \frac{x}{2} Then by doing some factorization of the top and bottom and some cancellations of terms you should get the desired result. I scribbled it out an a...

Are you looking for a basis for the subspace of all 2x2 matrices such that both entries in the second column are equal ? Or are you only dealing with a single particular matrix in which case saying "basis for the matrix" would make no sense. Generally when we refer to a basis with regards...

My apologies. I should have made clear that specified X = <x,y,z> is a position vector from the origin to a arbitrary point (x,y,z) in the plane. Vector X is not in the plane but the vector difference X-A is a vector in the plane and that vector dotted with the normal vector N to the plane = 0...