We are given with two matrices A, B of same order and a scalar k. How to prove that
Two matrices are equal if they have same order and their corresponding elements are equal.
Similarly, if we can prove that
and
have same order and their corresponding elements are equal then it means that equation
is true.
Lets first prove that
and
have same order.
Let order of A and B be m x n {They must have same order to be added}
Then, Order of A+B would also be m x n
Order of
would also be equal to m x n
Now, find out order of right hand side of equation
We have supposed order of A and B equal to m x n
Order of
would be equal to m x n and order of
would also be equal to m x n.
Order of
would be equal to m x n.
Therefore,
and
have same order.
Now, lets prove that
and
have equal corresponding elements.
element of
=
element of A +
element of B}
= k.
element of A + k.
element of B
=
element of kA +
element of KB
=
element of (kA+kB)
Therefore, we can say that corresponding elements of
and
are also equal. We have already proved that their order is same.
Therefore, equation
is true.
Mussab ali shah says
send me solution of second part