Matrices with the same corresponding entries look exactly identical. What do we say when two objects are identical using mathematical terms?
equal
We are asked to complete the following definition.
Two matrices are if all of their corresponding entries are equal.
Let's consider the following two 2* 2 matrices.
A=
1* 1 & sqrt(4)
13+1 & sqrt(3)
[1.3 em]
B=
2-1 & 2
2* 7 & sqrt(3)
Notice that if we simplify the entries of these matrices, they become identical.
A=
1* 1 & sqrt(4)
13+1 & sqrt(3)
=
1 & 2
14 & sqrt(3)
[1.3 em]
B=
2-1 & 2
2* 7 & sqrt(3)
=
1 & 2
14 & sqrt(3)
Since the matrices with equal entries can be simplified to identical matrices, we say that matrices with equal entries are equal.
A=B
Now we can complete the definition.
Two matrices are equal if all of their corresponding entries are equal.
