Question 4: Show that set of all real matrices of order m xn U11 U12 Uin ... U21 U21 и, 2n ... V = M ; U1,U12,U21,U..u e R } is a vector space. mxn mn ... ... ... Uml U mn Imxn ...

Elementary Linear Algebra (MindTap Course List)
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Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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Prove this in detail Need ASAP I vll upvote definitely but I need it urgently
Question 4: Show that set of all real matrices of order m x n
U12
Uin
...
и.
...
V = M
is a vector space.
mxn
mn
...
...
...
...
и,
Uml
'ml
...
mn Jmxn
Similar to the Mva, we can show that M.
is also a vector space.
mxn
Hint: We take 3 matrices
11
bin
C12
Cin
...
...
...
a21
A =
b21
B =
b1
b,,
& C =
a2n
C21
C21
C2n
2n
and
scalars
...
...
...
...
...
...
...
...
...
[aml
aml
a,
bml
b.
C.
mn
ml
m1
mn
mn
a, BeR.
v.s. [(Mmns R, +,)]
Transcribed Image Text:Question 4: Show that set of all real matrices of order m x n U12 Uin ... и. ... V = M is a vector space. mxn mn ... ... ... ... и, Uml 'ml ... mn Jmxn Similar to the Mva, we can show that M. is also a vector space. mxn Hint: We take 3 matrices 11 bin C12 Cin ... ... ... a21 A = b21 B = b1 b,, & C = a2n C21 C21 C2n 2n and scalars ... ... ... ... ... ... ... ... ... [aml aml a, bml b. C. mn ml m1 mn mn a, BeR. v.s. [(Mmns R, +,)]
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