Cayley- Hamilton Theorem : B.Sc. Mathematics : Linear Algebra #linearalgebra #cayleyhamiltontheorem

  For a video explanation, click here 👉 https://youtu.be/NIQCW-Jg9yo

 

                            Cayley-Hamilton Theorem : 

Statement : 

   Every square matrix satisfies its characteristic equation

Proof : 

    


 * Basis Extension Theorem 

 * V/W forms a vector space

 *  Show that the set { ( 1 , 2 , 1 ) , ( 2 , 1 , 0 ) , ( 1 , -1 , 2  } forms a basis of V3 ( F )

  

Comments

Post a Comment

Popular posts from this blog

sin30=1/2 : what it means? 🤔 #sin30, #trigonometry

Image
For a video explanation, click the link 👉  https://youtu.be/kXOzH8k_klw      we know sin30= 1/2.     what it means ?   🤔        In a right triangle if the sine of  angle  30  = 1/2   means that  "  the length of hypotenuse is always double the length of opposite side ". For Example ,  Suppose lenth of opposite side = 6 cm   then      lenth of its hypotenuse = 12 cm ***       Note :   If any one has any doubts in trigonometry or any mathematic concern topics please ask in the comment section .Also anybody of you want to give me friendly suggestions  post in the comment section. * what is dimension of an object? * 4th dimensional object Hypercube . * what is angle?   Page navigation #sin30 #= #1/2 #what #it #means #?  #maths #mathematics # trigonometry  #iit #jee #mains #eamcet #iit-jee #iitjee maths  #trigono...
Read more

INFINITE SERIES : #infinite #series #real #analysis

Image
                             INFINITE SERIES                                               Introduction                         P-Test                           Comparision test                          Limit Comparison Test                                                                      Cauchy's nth root test                                    ...
Read more

PROBLEM ON CHANGE OF ORDER OF INTEGRATION : DOUBLE INTEGRALS #double #integral #sum

Image
  *   Evaluate ∬ f(x,y) dxdy where f(x,y)= (2y-1)/ x+1 , and E is the region bounded by x=0,y=0, y=2x-        4.  *    Change the order of integration and hence show that ∬dx dy/[ ( 1+e^y) √(1-x^2-y^2)]   = (𝝿 /2)                    log(2e/(1+e) where x-0 to x=1 and y=0 to y=√(1-x^2)  *    In the integral ∬ (4-y) dydx, change the order of integration and evaluate the integral where x=2 to            x=4 and y=4/x to y=(20-4x)/(8-x)  *   Sketch the region of integration and evaluate ∬ xsiny dydx where x=0 to x=𝛑 and y-0 to y=x.  *   Sketch the region of integration and write an equivalent double integral with the order of integration      reversed for ∬ 3y dxdy where y=0 to y=1 and x= -√(1-y^2) to y=√(1-y ^2). *  Evaluate ∬ √(4x^2-y^2) dxdy where E is the region bounded by the li...
Read more