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

Linear spaces and subspaces, linear transformations, bases, etc.

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

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

jermy

Posts: 6
Joined: Tue Jun 18, 2013 9:05 am

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

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.
anonmeans

Posts: 58
Joined: Sat Jan 24, 2009 7:18 pm

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

Hi anonmeans,

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

Posts: 6
Joined: Tue Jun 18, 2013 9:05 am

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

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.
anonmeans

Posts: 58
Joined: Sat Jan 24, 2009 7:18 pm