Question

Suppose P is a 4 ×3 matrix, Q is an n × m matrix and R is a 3 × 2 matrix. If (QR)T PT is defined, then the size
of (PQR)T is

1. 5 × 2

2. 4 × 3

3. 2 × 4

4. 3 × 2

Answer 1

The n x m part is confusing me a lil. please explain if you can

Answer 2

ok lets say you have 2 matrices...one is size a x b , the other is m x n
the rule is you can only multiply them together if "inside" dimensions match
--> (a xb) (m x n) so only if b=m then the resulting matrix will be size (a x n)

so PQ -> (4 x3) (n x m) , since product matrix exists, assume n=3
resulting matrix is size (4 x m)

make sense?

Answer 3

cool, then will that make multiplying the last matrice R by the product of PQ (4 x m) = (4 x m) (3 x 2 )?

Answer 4

yep

Answer 5

So then the final outcome matrix should be a ( 4 x 2 ) ?

Answer 6

yes but then you have to transpose it

Answer 7

And does transposing any of the matrices change the positions of (n x m)

Answer 8

yes transposing basically flips the rows and columns of the matrix
(m x n) --> (n x m)

Answer 9

Oh that makes sense, so instead it becomes a ( 2x 4 )...thanx. Tell me is possible to transpose before i multiply or do i first have to multiply out then transpose?

Answer 10

multiply out , then transpose ....but it depends where they put the "T"
(QR)T ....at the end
(QT)R ... transpose Q first then multiply

Answer 11

oh i get it now. thanx