Equality Of Matrices

Two matrices are considered equal if and only if they meet both of the following conditions:

1. Same Dimensions (Order): They must have the same number of rows and the same number of columns.
2. Corresponding Elements are Equal: Every element in the same position in both matrices must have the same value.

The following diagram shows examples of matrices .

Let’s illustrate with examples:

Two matrices are equal if they have the same dimension or order and the corresponding elements are identical.

 

 

Matrices P and Q are equal.

 

 

Matrices A and B are not equal because their dimensions or order is different.

We can use the equality of matrices to solve for variables.

Example:
Given that the following matrices are equal, find the values of x, y and z .

 

Solution:
Equate the corresponding elements and solve for the variables.

x + 3 = 6
x = 3

y = −1

z − 3 = 4
z = 7

Equal Matrices and solving variables
Two matrices are equal if they have the same dimensions and all corresponding elements are equal.

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How to solve variables in equal matrices (equivalent matrices)?

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