Vector Subspace : Linear Algebra #vector #sub #space #linear#algebra

For a video explanation , click the link 👉https://youtu.be/ukbd5oWXMH4

                    

 Vector Subspace : Definition

       Let V(F) be a vector space and W ⊆ V. Then W is said to be a subspace of V if W           is   itself a vector space over F with the same operation of vector addition and                 scalar  multiplication in V. 

Example : 

        * The set of 2x2 triangular matrices is a vector subsapce of the space of all 2x2 

          with  matrices with real entries. 

 * What is a vector space

 * Theorem on vector space  

 * Historical Introduction to Linear Algebra






















































































































#vector #algebra #vector algebra   #iit #jee #mains #dimension #basis       

 #vector #space #linear#algebra #subspace  #sub                    


















                                   

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