- #1
Clandry
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Hi. I attached the problem and my work.
I'm not sure if I did part a) right. In the past problems I've done, they usually provide you with 3 vectors that are linearly independent, thus giving you unique values for C1, C2, C3. The matrix for this one forms:
1 1 1
0 1 3
0 0 0
Which is obviously linearly dependent.
In my work I solved it and C3 ended up canceling out. Does the free variable always cancel out when solving for T(vector) if the matrix above is linearly dependent?
For part b)
I said no, because if the 3rd element (element in 3rd row) in T(v) is nonzero, then the system is inconsistent.
I'm not sure if I did part a) right. In the past problems I've done, they usually provide you with 3 vectors that are linearly independent, thus giving you unique values for C1, C2, C3. The matrix for this one forms:
1 1 1
0 1 3
0 0 0
Which is obviously linearly dependent.
In my work I solved it and C3 ended up canceling out. Does the free variable always cancel out when solving for T(vector) if the matrix above is linearly dependent?
For part b)
I said no, because if the 3rd element (element in 3rd row) in T(v) is nonzero, then the system is inconsistent.