No complete answers please.
I know $\text{rank} \le \min(3, 3) = 3$
We have that the system is consistent, thus there are $3 - \text{rank}$ free variables.
But I cant progress further, help?
intersection of planes and rank of matrix
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linear-algebra
2 Answers
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Hint: Translate the planes $P_3,P_2,P_1$ to the origin so that now all three planes intersect along a subspace. What is the dimension of the intersection after the translation? How is it related to the rank of $A$?
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Hint:
Think along these questions.
If the rank is $0$, all the $a_i$ are $0$, is this the case here?
If the rank is $1$, the plane would have been parallel to each other.
If it is full rank, how many solutions will it intersect at? (hint: a non-zero small number)