How do i find the missing column of a matrix given the full RREF form?

In summary, to determine the missing column in a matrix given the full RREF form, one must look at the leading entries in each row of the RREF form. The dimensions of the original matrix are not necessary to find the missing column, and it is possible for a matrix to have multiple missing columns. The missing column can be found using only the RREF form, and there are no shortcuts or tricks to this process.
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Homework Statement



I'm given a 4x5 matrix with one missing column. I'm also given the RREF form with no missing columns.

Previous parts of the question made me find the row, column, and null basis for the matrix.

Now it's asking:

d) Find the missing column. (Hint: Are the columns of the matrix linearly independent or dependent?)

How would I go about finding the missing column? ^ What is the hint trying to get me to do? :s,

The rank of the RREF is 3, by the way.



Homework Equations





The Attempt at a Solution

 
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Related to How do i find the missing column of a matrix given the full RREF form?

1. How do I determine which column is missing in a matrix given the full RREF form?

The missing column in a matrix can be determined by looking at the leading entries (the first non-zero number) in each row of the RREF form. If a row has a leading entry of 0 or a row of all zeros, then that column is missing from the original matrix.

2. Do I need to know the dimensions of the original matrix to find the missing column?

No, the dimensions of the original matrix are not needed to find the missing column. The RREF form alone is sufficient in determining which column is missing.

3. Is it possible for a matrix to have more than one missing column?

Yes, it is possible for a matrix to have multiple missing columns. This can be determined by looking at the number of rows with leading entries of 0 or all zeros in the RREF form.

4. Can I find the missing column using only the RREF form, or do I need the original matrix?

The missing column can be found using only the RREF form. The original matrix is not needed as long as the RREF form is in its full and proper form.

5. Are there any shortcuts or tricks to finding the missing column of a matrix?

There are no shortcuts or tricks to finding the missing column of a matrix. It is a straightforward process of analyzing the RREF form and determining which column is missing based on the leading entries in each row.

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