Linear Algebra 10e: An Application of the Matrix Rank

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  1. MathTheBeautiful
  2. Linear Algebra (Field Of Study)
  3. Matrix Multiplication (Literature Subject)
  4. The Matrix (Award-Winning Work)
  5. Vector
  6. Linear Equation (Literature Subject)
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1:02, the columns are linearly dependent because the rows are linearly dependent. Is this true for all matrix? I am asking because what if we remove the third column and the matrix we have is 17 19, 10 20, 117, 219. The rows are linearly dependent but the columns are linearly independent.

RubberDuckyToy
Автор

All the columns have the linear property of a, b, a+10b right?

In that case, isn’t this video also an explanation of why columns with linear properties such as these, by taking their linear combinations, only can create other vectors with the same linear properties? (And thereby only span a subspace where all the vectors have this linear property)?

maxlilja