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**1. Homework Statement**

Find all possible values of rank(A) as

*a*varies.

A=[1, 2,

*a*]

[-2, 4

*a*, 2]

[

*a*, -2, 1]

A is 3x3, just merge the 3 row vectors.

**3. The Attempt at a Solution**

I have the solution but I create this thread to find the most effective/efficient procedure for me to solve these kinds of problems.

What are the possible dimensions of the row/column space as

*a*varies? When do the columns/ranks become linearly dependent based on different values for

*a*? I don't want to guess or plug in arbitrary numbers; I want a generalized, systematic approach that works every time.

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