Consider an augmented Matrix with 1508 unknowns. Which stmt is correct?

[blakesHue]

Hi,


I have some queries on this question. Since I can assume A to be any (2 by 1508) matrix, my conclusion is that option B , C and D are correct. (Please take note that the arrangement of the statements is C A B D.

Here is my reasoning:

First option aka C ) Can have a unique image if I set all the coefficient in matrix A to be 0 , except for the last unknown to be (x₁₅₀₈ and PI x₁₅₀₈ ) respectively, in such situation my unique solution is letting x₁₅₀₈ to be 1.

Second option aka A) Let matrix be a 0 matrix, no matter what the unknowns are, it will always be inconsistent

Third option aka B) Linear system is consistent because there a at least one set of answer to it, which as shown in the first option C.

Last option aka D) Linear solution has infinitely many solutions , means all my unknowns has infinitely set of solutions that satisfy the Right Hand Side(RHS), not sure if it is possible, but it seems workable

However, can the coefficient of any parameters in matrix A be PI ?

Need help solving this question.

Thank you.

 

[tkhunny]

Hi,


I have some queries on this question. Since I can assume A to be any (2 by 1508) matrix, my conclusion is that option B , C and D are correct. (Please take note that the arrangement of the statements is C A B D.

Here is my reasoning:

First option aka C ) Can have a unique image if I set all the coefficient in matrix A to be 0 , except for the last unknown to be (x₁₅₀₈ and PI x₁₅₀₈ ) respectively, in such situation my unique solution is letting x₁₅₀₈ to be 1.

Second option aka A) Let matrix be a 0 matrix, no matter what the unknowns are, it will always be inconsistent

Third option aka B) Linear system is consistent because there a at least one set of answer to it, which as shown in the first option C.

Last option aka D) Linear solution has infinitely many solutions , means all my unknowns has infinitely set of solutions that satisfy the Right Hand Side(RHS), not sure if it is possible, but it seems workable

However, can the coefficient of any parameters in matrix A be PI ?

Need help solving this question.

Thank you.

Suppose you multiply your row 1 coefficients (not all zero) by \(\displaystyle \pi\) to get your row 2 coefficients.

 

[blakesHue]

Suppose you multiply your row 1 coefficients (not all zero) by \(\displaystyle \pi\) to get your row 2 coefficients.

Yup, that sounds like a plan, which means there are many solutions to the question, now it seems that we can never have a unique solution because of the scaling by \(\displaystyle \pi\).

I think one of option C and A is incorrect (aka the correct answer for this mcq question since they are asking for incorrect)

I was wondering, can I have a (2 by 1508) matrix that are all zeros, if I could, then it would be option A correct as the linear system is consistent.