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Linear Algebra Confusion

Anonymous Thu 03 Dec 20:05:37 2020 No.12416222 View Reply Original Report

Quoted By: >>12416247 >>12416561 >>12417731

Is this system always inconsistent? That's what it looks like after all the work I've done on it. Did I do a good job? How would you rate my work?

Anonymous

Anonymous Thu 03 Dec 2020 20:09:15 No.12416239 Report

Quoted By: >>12416360

there are only three types of solutions in linear algebra:
no solutions
exactly 1 solution
infinite solutions

if you think it's the first case (i ain't doing your homework for you) then the equations define lines that are parallel.

if you think it's the second case, then the lines should intersect somewhere

if you think it's the third case, it's easy to show you can build linear combinations of solutions, and thus have an infinite number of solutions. the lines coincide.

plot them out if you have doubts. you are working in a low enough dimensional space that you can do that.

Anonymous

Anonymous Thu 03 Dec 2020 20:11:08 No.12416247 Report

Quoted By: >>12416277 >>12417391

>>12416222
wtf is inconsistent? Do you mean there's no unique solution? If that then there are a number of ways to check that the matrix has no inverse. The easiest is chechking of the determinant is zero.

Anonymous

Anonymous Thu 03 Dec 2020 20:18:21 No.12416277 Report

Quoted By: >>12416360 >>12416409

>>12416247
det(A) = ad - bc
2 * 3 = 6
-6 * -1 = 6
6 - 6 = 0
Does this mean there is no solution?

Anonymous

Anonymous Thu 03 Dec 2020 20:32:47 No.12416360 Report

Quoted By: >>12416597 >>12416619

>>12416277
it means it isn't invertible. considering >>12416239, either there is no solution or infinite solutions

Anonymous

Anonymous Thu 03 Dec 2020 20:40:43 No.12416409 Report

Quoted By:

>>12416277
Yup.

Anonymous

Anonymous Thu 03 Dec 2020 21:10:56 No.12416561 Report

Quoted By: >>12417240

>>12416222
Linear algebra was a long time ago for me, but it looks like there are infinite solutions.

Consider any pairs values for h and k, such that -3h = k

you have for instance 0 and 0, -1/3 and 1, etc etc

Usually when you make those row substitution you set the right hand side to a constant, but in this case you have another variable. But I might be retarded who knows

Anonymous

Anonymous Thu 03 Dec 2020 21:18:13 No.12416597 Report

Quoted By:

>>12416360
>it means it isn't invertible
I just checked this. If the determinant of a matrix is zero, then it can't be inverted, as the inverse of a square 2 x 2 matrix is 1/det(A) {{d, -b},{-c,a}}. This is because, as a transformation, that matrix brings down the rank of any vector it functions on. Correct me if I'm wrong, or if I'm forgetting to mention something.

Anonymous

Anonymous Thu 03 Dec 2020 21:21:25 No.12416619 Report

Quoted By: >>12417240

Anonymous

Anonymous Thu 03 Dec 2020 23:54:22 No.12417240 Report

Quoted By: >>12417570

>>12416619
This problem isn't about det(A) or invertability at all. This system is only consistent if the bottom row is a multiple of the first. Yes this does imply that A isn't invertible, but it also implies a million other things. >>12416561
Is right

Anonymous

Anonymous Fri 04 Dec 2020 00:36:10 No.12417391 Report

Quoted By: >>12417570

>>12416247
Inconsistent has nothing to do with invertible. Inconsistent mean's there is no solution.

Anonymous

Anonymous Fri 04 Dec 2020 02:02:54 No.12417570 Report

Quoted By:

>>12417240
>>12417391
I just found out the solution to the problem.
-3h = k
0 = k + 3h
If k + 3h were nonzero, the system would have no solution. Since k + 3h = 0, the system has an infinite number of solutions. The system is consistent for any values of h and k that make k + 3h = 0.

Anonymous

Anonymous Fri 04 Dec 2020 03:15:02 No.12417731 Report

Quoted By: >>12417845

>>12416222
Wtf is this "consistency" retardations?
Just find the null space you fucking fuckwit

Anonymous

Anonymous Fri 04 Dec 2020 04:01:41 No.12417845 Report

Quoted By:

>>12417731
brainlet spotted
learn your vocab or learn to use google

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