If A and B are matrices of the same order, then
cA + cB is __equal/not equal to___ c(B + A) and
cA − cB is __equal/not equal to___ c(B − A).

Question

If A and B are matrices of the same order, then
cA + cB is __equal/not equal to___ c(B + A) and
cA − cB is __equal/not equal to___ c(B − A).

love_to_love_you · Answer

I get confused when it comes to matrices

hartnn · Answer

you can factor out a constant from matrices.

pX+pY = p (X+Y)
pX-pY = p (X-Y)

bobo-i-bo · Answer

love_to_love_you · Answer

So they're both equal?

hartnn · Answer

1st one is equal.

are you sure about 2nd?

love_to_love_you · Answer

I didn't think it was equal for second but got confused

hartnn · Answer

in that link, look for 'Properties of Scalar Multiplication'

cA-cB = c(A-B)

and A-B is not same as B-A

love_to_love_you · Answer

So it isn't equal to?

hartnn · Answer

yes,
the 2nd one is "not equal to"

love_to_love_you · Answer

Alrighty, thank you :)

love_to_love_you · Answer

And thank you for the link @Bobo-i-bo

bobo-i-bo · Answer

One way we can think about it is like this:
$$cA-cB=cA+(-c)B=cA+(c(-1))B=cA+c((-1)B)=cA+c(-B)=c(A-B)$$

bobo-i-bo · Answer

Np ^_^