Dimension of a Solution Space to a Homogeneous Linear System

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In this video I demonstrate how to find the basis for the solution space to a homogeneous linear system. The dimension of the solution space is also determined.
  1. Larry Choraszewski "Mr. C"
  2. Dimension
  3. Subspace
  4. Vector Spaces
  5. Basis
  6. Basis Vectors
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Комментарии
Автор

Thank u bro literally saved me 3 hours before the midterm

spectre
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im not even from your university but you explained it so well in 1/10 of the time that my lecturer took to explain, thank

egemenefe
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Bruh this is so helpful. When you actually try to understand this, its totally easy. Thank you

arturk
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can we say that basis are the solution that satisfies system by writing its parametric equation ? (what i mean basis generates parametrical solution which satisfies the system)

eylmaz
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But how can it even have a basis when it should not be able to form a basis since it fails to be linearly dependent (it forms a nontrivial solution)?

parfittelcano
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Newbie here, why is rref all zeros on Row 2 and 3? shouldn't all rref have diagonal 1's and rest are 0s?

edizon
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How would you do this for a non homogeneous system?

samr
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so in other words you could say that the dimension of a solution space of a system of linear equations (SLE) is definend by n (Number of variables) - rank (of the SLE) = number of free Variables..

davidscherm
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Why do R2 and R3 columns be of zeros in rref?

monicahomwenga