Can Matrices AB, BA, CD, and DC be Evaluated?

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In summary, the person is asking for help with evaluating matrices and their products, specifically AB, BA, CD, and DC. They have provided the relevant equations for matrices A, B, C, and D and are unsure if it is possible to evaluate them. They are then informed that evaluating a single matrix means finding its value and evaluating matrices AB, CD, and DC simply means multiplying them. They are also informed that DC is not a possible multiplication due to the difference in the number of columns and rows.
  • #1
Buster617
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Homework Statement



Hi all. I am doing this work and can't seem to find any information on this in any of my notes or textbooks. The question is, "Evaluate (if possible) AB, BA, CD and DC", this is what i need some help with.
I also have further on the question, "Evaluate | u |, | v |, u . v and u * v", but this one i can do already so i don't need help with this one.

I know that a single matrix can't be evaluated exactly and since i can't find anything on evaluating either a single matrix or multiple matrices, i assume at the moment that, it is not possible to evaluate these from the first question either?

The relevant equations are below:

[tex]
A = \left(\begin{array}{c} 21 \ 60 & 2 \ 7 \end{array}\right)
[/tex]
[tex]
B = \left(\begin{array}{c} 4 \ -5 & 3 \ -2 \end{array}\right)
[/tex]
[tex]
C = \left(\begin{array}{c} 15 \ 3 \ 7 & 5 \ 12 \ 4 \end{array}\right)
[/tex]
[tex]
D = \left(\begin{array}{c} 3 \ 5 \ 15 & 1 \ -1 \ 7 & -5 \ 1 \ 8 \end{array}\right)
[/tex]Any help/ information would be greatly appreciated. Thanks
 
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  • #2
You seem to be having a problem with the word "evaluate". You certainly can evaluate a single matrix- its value is itself. Similarly, "evaluating" AB simply means finding the product of matrices A and B. AB, CD, and DC also mean just "multiply the matrices".
 
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  • #3
Ahh ok, i get it now. Thanks a lot.
Just done them all and they seem correct, I've still come up with DC not being possible due to there being a different number of columns in the first matrix compared to the number of rows in the second matrix.

Thanks again
 
  • #4
Yes, that is correct. DC is not a possible multiplication. (But CD is.)
 

1. What is a matrix?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. It is used to represent and manipulate data in many areas of mathematics and science.

2. How do you perform operations on matrices?

To perform operations on matrices, you must first ensure that the matrices have the same dimensions. Then, you can add, subtract, or multiply them using specific rules and formulas.

3. What is matrix multiplication?

Matrix multiplication is a mathematical operation that involves multiplying two matrices to create a new matrix. It is performed by multiplying each element of a row in the first matrix by each element of a column in the second matrix and then adding the products.

4. How do you evaluate a matrix?

To evaluate a matrix, you can perform various operations such as finding the determinant, inverse, or eigenvalues. These operations can provide valuable information about the matrix and its properties.

5. What are some real-life applications of matrices?

Matrices have many real-life applications, such as in computer graphics, data analysis, and optimization problems. They are also used in physics, engineering, and economics, among other fields, to model and solve complex systems and equations.

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