Question

Tell whether the product CD is defined for C9x5 and D5x9. If yes, give the product's dimensions as the following example: 2x3. If no, write no in the box

Answer 1

What are the inner dimensions of C_(9x5) D_(5x9) ?

Answer 2

ive no idea

Answer 3

\(\color{brown}{\text{these}}\) ones
\[C_{9\times\color{brown}5}D_{\color{brown}5\times 9}\]

Answer 4

i dont know how to calculate the dimensions

Answer 5

the inner dimensions are both 5, so we can take the product of the matrices,
the resulting matrix will have the outer dimensions

Answer 6

how do you do that

Answer 7

one way to think about it is
that the 5's cancel and the 9's are left over.
i.e. the resulting matrix will be 9x9

Answer 8

how do the 9s not cancel out each other

Answer 9

fortunately we do not have to calculate the element of this large (9 rows and 9 column ) matrix

Answer 10

the 9's don't cancel because they are on the outside

Answer 11

ohhhh i see

Answer 12

if we multiplied the matrices the other way around i.e.

D_(5x9) C_(9x5)

the result will be a 5 x 5 matrix

Answer 13

ahhh i see now

Answer 14

thanks c:

Answer 15

I that question before, with the two tables

we were multiplying row and column vectors like this

R_(1x3) P(3x1) = some (1x1) matrix i.e. the total

Answer 16

so its 1 x 1

Answer 17

yeah a number (a scalar) like 249.7 is a degenerate matrix

Answer 18

i see

Answer 19

wait a minute so how did you calculate all this