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?