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In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank should be as large as possible. Explain why an $m \times n$ matrix with more rows than columns has full rank if and only if its columns are linearly independent.

This happens if and only if the columns of $A$ are linearly independent.

Calculus 3

Chapter 4

Vector Spaces

Section 6

Rank

Vectors

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problem. 26. Um, we need to explain that if we have ah, and and by n Matrix with more rose than the columns as four rank, then this is an equivalent statement as saying that the columns are linearly independent. So again we're give or if we know that the columns are we nearly independent for matrix, the columns are linearly independent. So that actually means Wait a moment, how to write down this. So that is equivalent to say All columns are people comes and so she's all whole columns are people columns. So we know that the rank is the number of cops which in this case, it's in Okay. And again we recall that we call that rank off. Eh? Ran cafe is the minimum up The row broke rose and the number of columns. And in this case, we know that we have more rows and columns so than the minimum of feminine should be. And so all these all these statements are equivalent so we can conclude that that way we have ah matrix setting with more roses than columns and has a full rank. Then this is the equipment to say the columns are we nearly did not independent

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