Matrices

[msjoharia]

Indicate whether the statement is true (T) or false (F).

Justify your answer.

(a) If
AB and BA are both defined, then A and B are


square matrices.
(b) If

AB + BA is defined, then A and B are square


matrices of the same size.

(c) If
B has a column of zeros, then so does AB if this


product is defined.

(d) If
B has a column of zeros, then so does BA if this


product is defined.

(e) The expressions tr
(ATA) and tr(AAT ) are defined for


every matrix
A.


(f ) If
u and v are row vectors, then uTv = u ・ v.

 

[renegade05]

Indicate whether the statement is true (T) or false (F).

Justify your answer.

(a) If
AB and BA are both defined, then A and B are


square matrices.
(b) If

AB + BA is defined, then A and B are square


matrices of the same size.

(c) If
B has a column of zeros, then so does AB if this


product is defined.

(d) If
B has a column of zeros, then so does BA if this


product is defined.

(e) The expressions tr
(ATA) and tr(AAT ) are defined for


every matrix
A.


(f ) If
u and v are row vectors, then uTv = u ・ v.

You can't just post a bunch of problems on here expecting people to give you the answer. I helped you out on your other thread, but come on man... show some effort.