Is b in the column space of A and is the system consistent?

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SUMMARY

The discussion centers on determining if the vector b = [4, 8] is in the column space of the matrix A = [[1, 2], [2, 4]]. It concludes that the system Ax = b is consistent, as there are infinitely many solutions. The key to confirming b's presence in the column space lies in expressing b as a linear combination of the columns of A, which is achievable given the relationship between the elements of A and b.

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1. Homework Statement [/b]

For each of the following choices of A and b, determine if b is the column space of A and state whether the system Ax=b is consistent

A is a 2 by 2 matrix , or A=(1,2,2,4) , 1 and 2 being on the first row and 2 and 4 on the second row. and b=[4,8] 4 being on the first row and 8 being on the second row . Ax=b

Homework Equations





3. The Attempt at a Solution

I know the system is consistent , because the system has infinitely many solutions. I haven't the first clue of how to determine if b is in the column space of A .
 
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Can b be expressed as a linear combination of the columns of A? If the system is consistent, well...
 
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