Combine two different size matrix in state equations

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Homework Help Overview

The discussion revolves around combining two sets of state equations represented by matrices of different sizes. The original poster presents two state equations with matrices A, B, and C, questioning the feasibility of adding these matrices due to their differing dimensions.

Discussion Character

  • Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants inquire about the definitions and dimensions of matrices A, B, and C, as well as the nature of the vectors x, y, and u. There is a discussion about the possibility of adding matrices of different sizes and the implications of scalar addition.

Discussion Status

The original poster initially expresses confusion regarding the addition of matrices of different sizes but later indicates they have resolved their misunderstanding regarding the addition of a scalar to a matrix. Another participant suggests a different approach involving the identity matrix, indicating ongoing exploration of the topic.

Contextual Notes

There is a lack of clarity regarding the definitions of the matrices and vectors involved, which may affect the understanding of the problem. The original poster's realization about scalar addition highlights the importance of matrix dimensions in operations.

khedira
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i have two sets of state equations:

1) x(dot) = (2x2)x + (2x1)u
y = (1x2)x

2) x(dot) = (0)x + (1x1)u
y = (1x1)x

given the above, since A, B and C are of different sizes, how can i add the A from 1) and 2) to get a combined A? Is that possible? Please advise. Thank you.
 
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what are A, B & C? can you explain better?

also what are x,y & u are these 2x1 column vectors etc.
 
lanedance said:
what are A, B & C? can you explain better?

also what are x,y & u are these 2x1 column vectors etc.

Hi lanedance,

Thank you for your reply. I confused myself and is able to get the answer already.

The problem was that i have this A1 2x2 matrix, e.g. [1 2; 3 4] and i have another A2 1x1 matrix [5]. I wish to add them together, i.e. A = A1 + A2. At first i thought that the size different between A1 and A2 make it impossible to directly add them up. Then i realize that since A2 is in scalar form, A = A1 + A2 = [6 7; 8 9].

Thank you for your reply anyway.
 
yeah that doesn't seem quite right, maybe if its A2*I , where I is the identity matrix it works
 

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