Question
Asked Aug 30, 2019
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PLEASE BE AS BASIC AND SIMPLE AS POSSIBLE FOR ME. 

PLEASE, I NEED A DETAILED STEP-STEP PROCESS WITH EX
PLANATIONS TO THIS QUESTION
(I have no
for me.) THANK YOU
as much as possible
prior knowledge in Algebra, so be simple
Let K be a field
(1) prove that for all m, n 2 1, one has Km,n
Kmn
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PLEASE, I NEED A DETAILED STEP-STEP PROCESS WITH EX PLANATIONS TO THIS QUESTION (I have no for me.) THANK YOU as much as possible prior knowledge in Algebra, so be simple Let K be a field (1) prove that for all m, n 2 1, one has Km,n Kmn

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Expert Answer

Step 1

Consider T,

a12
1n
a2a2
T
mpcn
a
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a12 1n a2a2 T mpcn a

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Step 2

To prove that T is linear, one-to-one and onto.

First prove for linear trasformation as follows.

ab ab
+
2n
T ab
+
ab a +b
ml
m2
m2
ab
bin
in
b b2
am2
ml
mmmn
+T
ml
.
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ab ab + 2n T ab + ab a +b ml m2 m2 ab bin in b b2 am2 ml mmmn +T ml .

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Step 3

Now prove for scalar m...

:
ра,
ра,,
ра,
ра
рал
ра,
ра,2
a
pa
ра
ра ра,
a
ml
m2
pa
a
a22
= p
mn
= pT
mn
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: ра, ра,, ра, ра рал ра, ра,2 a pa ра ра ра, a ml m2 pa a a22 = p mn = pT mn

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