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I've attached the problem.

for the 1st part:

I solve the system for det(A)=0 and find the values of a that the system DOES NOT have an unique solution.

This ended up being a=0, -2, 2

Thus the answer would be a≠0, -2 , 2

For the 2nd part:

I must rearrange the matrix A such that the last column [0 0 1]^T is the rightmost column of an augmented matrix.

I then find RREF of this matrix. In order for the last column to be a linear combo of the 1st 2, there must be no free variables in the 1st 2 columns. I'm not too sure how to row reduce this problem though since we have a variable a in there. I can tell that a=0 is one of the answers by inspection. a can't equal another other scalar because that will yield an inconsistent system. Thus, a=0 should be the only answer.

How do I approach this problem by row reducing? because not all problems can be solved by inspection.

This problem was a practice problem from last year's exam. It was 1 of 6 problems on the 50 minute test. The problem is it took me like 20minutes just to do this problem (However, I have not done any reviewing yet.) The second part took under a minute, but the second part just took me a while to figure out what is going on.

Also, on a side note, the vector b is not used to solve these 2 parts right?

for the 1st part:

I solve the system for det(A)=0 and find the values of a that the system DOES NOT have an unique solution.

This ended up being a=0, -2, 2

Thus the answer would be a≠0, -2 , 2

For the 2nd part:

I must rearrange the matrix A such that the last column [0 0 1]^T is the rightmost column of an augmented matrix.

I then find RREF of this matrix. In order for the last column to be a linear combo of the 1st 2, there must be no free variables in the 1st 2 columns. I'm not too sure how to row reduce this problem though since we have a variable a in there. I can tell that a=0 is one of the answers by inspection. a can't equal another other scalar because that will yield an inconsistent system. Thus, a=0 should be the only answer.

How do I approach this problem by row reducing? because not all problems can be solved by inspection.

This problem was a practice problem from last year's exam. It was 1 of 6 problems on the 50 minute test. The problem is it took me like 20minutes just to do this problem (However, I have not done any reviewing yet.) The second part took under a minute, but the second part just took me a while to figure out what is going on.

Also, on a side note, the vector b is not used to solve these 2 parts right?