Vector Spaces Question (I think?),
Question is here:
https://i.imgur.com/m8TtMqD.png

Completely lost anyone able to help me understand what the questions mean in particular what ⊗ and ⊕ is?

Furthermore, how I can so such a property as the one depicted in the question?

Question

Vector Spaces Question (I think?),
Question is here:
https://i.imgur.com/m8TtMqD.png

Completely lost anyone able to help me understand what the questions mean in particular what ⊗ and ⊕ is?

Furthermore, how I can so such a property as the one depicted in the question?

aum · Answer

⊗ is multiplication.
They have given you their definition of how to multiply a matrix by a scalar k.
Follow that definition and evaluate each of the three multiplications.  Then do the matrix addition of the right hand side and see if it matches the left hand side.

aum · Answer

Note: This is not the accepted way to multiply a matrix by a scalar.  They have altered the definition of scalar multiplication just for this problem.  They have a provided a new definition of scalar multiplication.  If you follow that rule they are asking if the last lline is true or not.  Just follow their definition.  Multiply each matrix following their definition.  Then add the two matrices on the RHS.  See if it matches LHS.

australopithecus · Answer

ok ok I think I get what you mean, let me try, I will post my work

aum · Answer

Alright.

australopithecus · Answer

Does this look right @aum?

australopithecus · Answer

https://i.imgur.com/721EVrW.png

aum · Answer

Yes.  Good job!

australopithecus · Answer

Thanks for the help I appreciate it totally out of my mind right now so tired.

aum · Answer

You are welcome.  Well done.