Questions asked by kumail

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• What's the value of a matrix raised to the -1 power?
  
• Whats the "trace" of a Matrix?
  
• How can I divide two matrices together?
  
• Find the matrix A (in terms of B, C, and D)?
  
• How do I calculate the determinant of a 4x4 Matrix?
  
• What are eigenvectors and eigennumbers?
  
• How to evaluate `int ln(1-x^9)dx` as a power series?
  
• Is the set of all 3 × 3 matrices that have the vector `[2, 1 , -2]^T` as an eigenvector closed under addition?
  
• Is the set of all polynomials in `P2` of the form `a_0 + a_1  x + a_2  x^2` where `a_0 = a_2 ^2` closed under addition?
  
• Is the set of all vectors in `R2` of the form `(a, b)` where `b = a` closed under addition?
  
• Is the set of all `2 × 2` matrices whose trace is equal to `0` closed under scalar multiplication?
  
• Does the set `p_1=1,p_2=1−3x,p_3=x,p_4=x^2` form a basis for `P2`?
  
• In a nutshell, my question is that why does wearing shoes while dealing with electricity not get me shocked. Thanks u very much. i have my Ph.D exam in Physical Engineering, thanks 4 help?
  
• How can I find the shortest distance between the point `(0,1,-1)` and the line `(x,y,z) = (2,1,3) + t(3,-1,-2)`?
  
• Find all complex roots of `z^3= -8i`?
  
• How can I check if a given line lies in a given plane or not?
  
• How can I find the projection of a vector onto a subspace?
  
• If det(A) = 7, what is det(Adj(A))?
  
• What is the maximum rate of change of `f(x,y) = y^2/x` at the point `2,4`?
  
• Find the length of the parametric curve `x = e^t + e^-t, y = 5 - 2t` from `t = 0 to t = 1`?
  
• What's the second derivative of `x = t^2 + t, y = e^t`?
  
• Solve `dy/dx = r-ky` ?
  
• What's the curve parallel to the parabola `y=x^2`?
  
• Which element is oxidized and which is reduced?
  
• Density of a solution?