Matrix Variables: Solving Mx = b with 2-D Vectors

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The discussion centers on solving the matrix equation Mx = b, where M is a 4x2 matrix with a rank of 2. Participants confirm that the vector x consists of only two elements, x1 and x2, due to the rank limitation. The correct representation of vector x is x = [x1, x2]ᵀ, indicating a transposed column vector. This clarification is crucial for understanding the dimensionality of solutions in linear algebra.

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  • Understanding of linear algebra concepts, specifically matrix rank
  • Familiarity with matrix notation and operations
  • Knowledge of vector representation in mathematical contexts
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EvLer
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if I am given this to solve:
Mx = b
where M
[0 0]
[1 2]
[0 0]
[3 6]

and b = [b1, b2, b3, b4]t

does that mean I have vector x as 4 elements, i.e. x1-x4 or just x1 and x2?

thanks

edit: oh, wait... rank is 2, so its only x1 and x2, right?
 
Last edited:
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Your vector will be x=[x1 x2]T
 
oh, didn't refresh in time... thanks :)
 

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