Consider two matrices with equal corresponding elements. What can you say about them?
equal
Practice makes perfect
We are asked to complete the following sentence.
If corresponding elements of matrices are equal, the matrices are ?.
First, let's think about when two matricescan have corresponding elements. Consider matrices A and B that are defined as follows.
A = 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 and B = 1 & 2 3 & 4
Now, let's have a look at the first rows of the matrices. We could say that 1 corresponds to 1 and 2 corresponds to 2. However, which element from matrix B would 3 correspond to? There is no such element in B. These matrices do not have corresponding elements, because they have different dimensions. Let's consider matrix C that has the same dimensions as A.
A = 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 and C = 2 & 8 & 0 5 & 9 & 7 0 & 1 & 8
Notice that now we can say which elements correspond to each other.
Element from A
Element from B
1
2
2
8
3
0
4
5
5
9
6
7
7
0
8
1
9
8
Looking at the given sentence again, we can tell that we want to consider a situation when corresponding elements of matrices are equal. Let's now consider a matrix D with elements that are equal to the elements from matrix A.
A = 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 and D = 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9
We can see that these matrices are the same, so we can say that they are equal. Finally, we can complete the given sentence.
If corresponding elements of matrices are equal, the matrices are equal.
