Ring Theory: ua-cam.com/video/vxc5bUzmspY/v-deo.html ua-cam.com/video/6otAOx2VNoY/v-deo.html Linear Transformation Playlist: ua-cam.com/play/PL_RrZ82fmpNWvMeHyFnlfK_e8T6Ekk_fa.html
All points on X-axis are common to XY-plane and X-axis. For example:- (1,0,0), (0,0,0), (-6,0,0)...etc. So there are infinite points common to X-axis and XY-plane. Hence XY-plane +X-axis is not direct sum. But only (0,0,0) is common to X-axis and Y-axis ,hence X-axis+Y-axis is direct sum.
Q.29 main W vector addition property satisfy nehi kar raha hai.. suppose ek example W1= 1 0 0 -1 And another is W2= 2 0 0 1 Then 3 0 0 0 Satisfy nehi kar raha hai
W and U are subspaces. We have W= x1 0 0 x2 Here x1 and x2 can be any real number. So x1 and x2 can be zero. Hence 3 0 0 0 belongs to W. Likewise 0 0 0 0 0 0 , 0 3 etc also belongs to W. So W is closed under addition and closed under scaler multiplication. And hence W is Subspace. In the same way U is also a subspace.
Q.28 , option a is correct
Thank you for this study content☺️
Great sir after seeing these 7 lecture my confidence is boost for my exam thanku guruji ❤❤💗
This is the best way to do practice.. Thankyou sir 😊😊
Your teaching style is very good keep goong
Sir your videos are very helpful ❤ thank you for uploading this study content 🙏
Sir msc maths ke liye lucknow university entrance exam ka prepration kise kre samjh me nhi aa rha h😔😔
Sir ji bhot bhot acha padaya
I have completed both parts of vector space
Where is the pdf uploaded?
❤❤❤
sir. prime ideal and maximal ideal...ring...zero divisor..ideal test..integral domain. mcqs...send
Ring Theory:
ua-cam.com/video/vxc5bUzmspY/v-deo.html
ua-cam.com/video/6otAOx2VNoY/v-deo.html
Linear Transformation Playlist:
ua-cam.com/play/PL_RrZ82fmpNWvMeHyFnlfK_e8T6Ekk_fa.html
Sir complete upload karna linear algebra
Very helpful thanku
Sir agar alpha, bita and gamma have infinite solutions then span belongs hoga 😢
Isska pdf kahan milega sir
Sir pdf milega isko ?
Q-28
Ans -(a) only (ii) is correct
28 option a correct
Sir can u please upload both papers 1&2 all chapters mcq of 6th semester before our exam
Yes i will upload before exam.
Thanks 🙏
Thanku so much sir❤❤
Nice sir ❤
Sir Q#41 C over field R is not a vector space the how we find the dimension of said Question ❓
set of complex numbers (C) is a vector space over field of real numbers (R).
So it has dimension.
Thanks sir
q no. 28. option a
❤
28. option a is correct.
Sir q.43 m dim V =4 hogi n ....?
Yes.. correct.
Dim V=4
Dim W=1
@@KTexplains thank you sir
mra paper 28 sa start hy..plz all mcqs send
Options (a) is correct
Q.28
Right
hy...ap ka kon sa semester hy...
Thanks 🙏❤
Please upload the file so we can printout and revise..
Thank you Sir
Qus 42 me number of vector to 3 hai fir dim w= 1 kese aya??
27:21
B={(1,1,1)}
(1,1,1) means number of vector is 1 with 3 components.
@@KTexplains 🙏thankyou sir
Xy plane and x axis.... Common... , (0, 0,0) will come... Is it correct sir
All points on X-axis are common to XY-plane and X-axis.
For example:- (1,0,0), (0,0,0), (-6,0,0)...etc.
So there are infinite points common to X-axis and XY-plane.
Hence XY-plane +X-axis is not direct sum.
But only (0,0,0) is common to X-axis and Y-axis ,hence X-axis+Y-axis is direct sum.
Thank you sir
Q.29 main W vector addition property satisfy nehi kar raha hai.. suppose ek example W1=
1 0
0 -1
And another is W2=
2 0
0 1
Then
3 0
0 0
Satisfy nehi kar raha hai
W and U are subspaces.
We have
W=
x1 0
0 x2
Here x1 and x2 can be any real number.
So x1 and x2 can be zero.
Hence
3 0
0 0 belongs to W.
Likewise
0 0 0 0
0 0 , 0 3 etc also belongs to W.
So W is closed under addition
and closed under scaler multiplication.
And hence W is Subspace.
In the same way U is also a subspace.
@@KTexplains meri explanation thik hai naa
@@suvasmitasahoo1791 but 0 is also in R so is subspace
28 option A
I think option no 3 is correct
Suppose if you take (1, 2,3) it cannot be expressed as a linear sum of x and y axis...
28... Ans, option d sir... Is it right sir
Option (a) is correct.
28 ka a ans hoga
...
Thank you sir