Matrix addition

In summary, matrix addition is a mathematical operation where two matrices of the same size are added together by adding their corresponding elements. This results in a new matrix with the same dimensions as the original matrices. To perform matrix addition, the matrices must have the same number of rows and columns. It is not possible to add matrices of different sizes. The properties of matrix addition are commutativity, associativity, and distributivity, making it a versatile operation for solving equations and working with data. In real life, matrix addition is used in fields such as physics, engineering, and computer graphics for various purposes such as solving equations, performing transformations, and handling data in machine learning algorithms.
  • #1
johncena
131
1
Ques.)-If A,B,C are three matrices such that A+B = A+C, then prove that B=C.

Can i cancel out the A's in LHS and RHS ?
 
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  • #2
Yes, but...

Normally, a question like this is an exercise in demonstrating how useful operations (e.g. cancellation) can be derived from definitions or through the application of more basic properties.

If cancellation is on the list of basic properties you're using for this purpose, then citing that is all you need to do -- but I suspect the problem is not meant to be so trivial.
 

1. What is matrix addition?

Matrix addition is a mathematical operation where two matrices of the same size are added together by adding their corresponding elements. This results in a new matrix with the same dimensions as the original matrices.

2. How do you perform matrix addition?

To perform matrix addition, the matrices must have the same number of rows and columns. Then, simply add the corresponding elements of the two matrices and place the result in the corresponding position of the new matrix.

3. Can you add matrices of different sizes?

No, matrices of different sizes cannot be added together. Matrix addition is only possible when the matrices have the same dimensions.

4. What are the properties of matrix addition?

The properties of matrix addition are commutativity, associativity, and distributivity. This means that the order in which matrices are added does not matter, and that addition can be performed on multiple matrices at once.

5. How is matrix addition used in real life?

Matrix addition is used in various fields such as physics, engineering, and computer graphics. It can be used to represent and solve systems of linear equations, perform transformations in 3D graphics, and handle data in machine learning algorithms.

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