matrix transpose equation

[math2020]

hi
assume A & B are matrix does this

A'(A-B)=(A'-B')A
is true...is both side equal?? yes or no

 

[Romsek]

hi
assume a & b are matrix does this

a'(a-b)=(a'-b')a
is true...is both side equal?? Yes or no

\(\displaystyle (ab)^t = b^t a^t\)

\(\displaystyle a^t(a-b) = ((a-b)^ta)^t\)

so the equation is false unless \(\displaystyle a\) and \(\displaystyle b\) are symmetric

i.e. \(\displaystyle a^T=a,~b^T=b\)

 

[Romsek]

\(\displaystyle (ab)^t = b^t a^t\)

\(\displaystyle a^t(a-b) = ((a-b)^ta)^t\)

so the equation is false unless \(\displaystyle a\) and \(\displaystyle b\) are symmetric

i.e. \(\displaystyle a^T=a,~b^T=b\)

btw the TeX editor clobbered my capital letters. Is there a way to prevent that?

 

[Steven G]

hi
assume A & B are matrix does this

A'(A-B)=(A'-B')A
is true...is both side equal?? yes or no

Why not pick two matrices and test it for yourself?

We just do not give out answers but rather we prefer to help. You were lucky this time that someone solved this problem for you. Do you understand their work?