Question

find non zero matrices A,B and C such that AC=BC find non zero matrices A,B and C such that AC=BC @Mathematics

Answer 1

I'm betting there is more to this problem....

Let A=B

Answer 2

for example let A=B=C=I

Answer 3

yes u r right A is not equal to B

Answer 4

\[A=\left[\begin{matrix}1 & 0 \\ 0 & 0\end{matrix}\right]\]
\[B=\left[\begin{matrix}0 & 0 \\ 1 & 0\end{matrix}\right]\]

\[C=\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]\]

Answer 5

are u take these matrices by applying any rule if so then plz tell me how such matrices are taken

Answer 6

the only thing I really need to do was to make sure that C was not of full rank

Answer 7

what is meant by 'C is not of full rank'?

Answer 8

In the case of square matrices ...I needed to make sure C was not invertible. then it was easy to find and A and B that worked

Answer 9

http://en.wikipedia.org/wiki/Rank_(linear_algebra)

Answer 10

u mean A and B must be invertible but C is not invertible and we take any matrices by applying this rule

Answer 11

no...since clearly the none of the matrices I gave are invertable

Answer 12

ok we can take only singular matrices of any order and with different entries isn't it?

Answer 13

\[A=\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]
\[B=\left[\begin{matrix}1 & 0 \\ 1 & 1\end{matrix}\right]\]
\[C=\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]\]

Answer 14

the above works...and A,B are both invertable

Answer 15

in this case C is singular which i have already told

Answer 16

yes...C has to be singular otherwise it is impossible

Answer 17

briefly A and B may or may not be singular but C must be singular am i right?

Answer 18

no

Answer 19

what do u want to say?

Answer 20

sorry..yes...A,B could be singular or not, but C has to be singular

Answer 21

but your choice of A and B is still limited...not all A,B work

Answer 22

thanks a lot

Answer 23

no problem

Answer 24

how choice of A and B is limited

Answer 25

it has to do with the null space of C