Suppose 3 planes of the form $AX=b$ intersect at a unique point. Suppose in this case $b= (1,1,1)$. In case $b$ is changed to $(2,3,4)$ or any other vector, will the planes still intersect at a unique point?


closed as off-topic by GNUSupporter 8964民主女神 地下教會, Nosrati, Davide Giraudo, Namaste, KReiser Dec 8 '18 at 0:21

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Davide Giraudo, Namaste, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    $\begingroup$ Is $A$ a vector or a matrix? As written, each row of $A$ corresponds to the coefficients of a plane. What are your thoughts? $\endgroup$ – Michael Burr Dec 7 '18 at 12:01

In the first case the rank of $[A \ b]$ is $3$ (unique solution) and the system is consistent. So rank of $A $ is $3$. So any point/vector $b\in\mathbb {R}^3$ can be expressed as a linear combination of columns of $A $. Equivalently there is a unique solution.


Not the answer you're looking for? Browse other questions tagged or ask your own question.