Matrix(algebra): prove (A + B)^T = A^T + B^T

Linear spaces and subspaces, linear transformations, bases, etc.
jermy
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Matrix(algebra): prove (A + B)^T = A^T + B^T

Postby jermy » Tue Jun 18, 2013 11:09 am

Can you please help me to solve the below proof

1. (A + B)^T = A^T + B^T

thank u in advance

anonmeans
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Re: Matrix(algebra): prove (A + B)^T = A^T + B^T

Postby anonmeans » Tue Jun 18, 2013 11:49 am

jermy wrote:Can you please help me to solve the below proof

1. (A + B)^T = A^T + B^T

Do the unspecific name for the entries, like "a-ij + b-ij", so the transposes are like "a-ji + b-ji". Then show that it is the same for the sum of the transposes. So just do the definitions.

jermy
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Re: Matrix(algebra): prove (A + B)^T = A^T + B^T

Postby jermy » Mon Jun 24, 2013 6:27 am

Hi anonmeans,

Actually i got this question in my math book and i cant do this.so please help me

anonmeans
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Re: Matrix(algebra): prove (A + B)^T = A^T + B^T

Postby anonmeans » Mon Jun 24, 2013 11:43 am

jermy wrote:Actually i got this question in my math book and i cant do this.so please help me

If you got this from your book then you have a book with definitions. what's the def. of "transpose"? Do that def. to both sides of the eqn. Show that they're the same which means the sides are equal.


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