Matrix Operations: Solving for A+B, AB, BA, AC, and CA

  • MHB
  • Thread starter karush
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In summary, A, B, and C represent variables or numbers being manipulated in the equation 2.3 Find A+B, AB, BA, AC, CA. The notation A+B, AB, BA, AC, CA represents different mathematical operations being performed on these variables. Finding these values allows for a better understanding of their relationships and how they can be manipulated. These operations have practical applications in fields such as chemistry, physics, and biology.
  • #1
karush
Gold Member
MHB
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https://www.physicsforums.com/attachments/8970
ok I think I did these are ok but knowing how tedious it is might be some typos
also does this work if you have different unequal rows for example if A had 3 rows and B had 2 rows

the pic is just a snip from my overleaf doc. I used macros to avoid long latex code in the bmatrix

mocho mahalo
 
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  • #2
They look good go me. Well done!
 
  • #3
make me feel young again !
 

1. What is the purpose of finding A+B, AB, BA, AC, and CA?

The purpose of finding these values is to perform basic operations on matrices, which are used to represent data in many scientific fields. These operations allow us to manipulate and analyze data in a more efficient and organized manner.

2. How do you find A+B?

To find A+B, we simply add the corresponding elements of matrices A and B. This can only be done if the matrices have the same dimensions.

3. Can you multiply matrices AB and BA?

No, matrix multiplication is not commutative, meaning the order of multiplication matters. AB and BA will result in different values unless one of the matrices is a scalar (a single number).

4. What is the difference between AC and CA?

The difference between AC and CA is the order in which the matrices are multiplied. In AC, matrix C is multiplied on the right side of matrix A, while in CA, matrix A is multiplied on the right side of matrix C. This can result in different values, as matrix multiplication is not commutative.

5. How can these operations be useful in scientific research?

These operations are useful in scientific research because they allow us to manipulate and analyze data in a more organized and efficient manner. Matrices are commonly used to represent data in fields such as physics, biology, and economics, and performing operations on them can help us draw conclusions and make predictions based on the data.

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