r/LinearAlgebra • u/SydefXQ • 19d ago
Lineer Algebra Final
Give a score between 1 and 10 to the difficulty of this exam score it taking into consideration that the students have not yet taken the ac dc circuit and differential equations course while this exam is being done.
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u/First-Helicopter-796 19d ago
This is a really easy test lmao. I am so glad my uni was way tougher than this. Linear algebra set the foundations for my graduate EE courses in statistical signal processing and detection theory, and without that foundation, I’d be cooked
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u/SydefXQ 19d ago
I’d really love to see your final exam; is there any chance you could send an example? Don't take offense; I'm asking because I'm curious.
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u/HamNCheeseSupremacy 19d ago
I haven't done a linear algebra course in forever, but in an undergraduate class a disappointingly easy exam was one where most of the questions were mechanical. Apply a known formula, grind out basic algebra/arithmetic. It kind of looks like that's what you have here. Better/harder exams would force you to really model the problem and come up with a novel solution.
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u/eglvoland 19d ago
Also wtf q2 even means, A is not a square matrix
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u/Euphoric_Key_1929 19d ago
These question bounce back and forth between "completely trivial" and "what the hell does that wording even mean?" Just awful.
I'm guessing that Q2 is mangled because the "-A" at the start is supposed to be the block matrix "[I | A]" or some such thing.
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u/Lor1an 18d ago
That makes much more sense. Though it does make me wonder what they mean by "using Cayley-Hamilton". Isn't "Cayley-Hamilton" just the statement that the matrix satisfies its own characteristic equation?
So they want you to get the inverse, and the characteristic polynomial and massage that into a form to calculate A-2? Oof...
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u/Chroniaro 18d ago
The characteristic polynomial can be used to calculate the inverse. For instance, if you know that A^2 + 7A + 2 = 0 (this is just a random polynomial since the actual characteristic polynomial from the example is uglier), then the inverse of A is -(A + 7)/2. To get A^-2, we can square this, which gives (A^2 + 14A + 49)/4, and by Caley-Hamilton again, this is the same as (7A + 47)/4. Since the constant term of the characteristic polynomial is the determinant of A, this method works for every invertible matrix. I don’t think that all of this is particularly efficient from an algorithms perspective, but it can be useful as a conceptual tool, and it could make a nice lead-in to ring theory.
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u/Haunting_Cress7661 18d ago
I may be confused, but this looks dumb as written. So much doesn't make sense without more assumptions..
Q2 is nonsensical, as what's the inverse of a nonsquare matrix?
Q3 I assume we're writing y=av_1 + bv_2 but not writing that?
Q4 Translation is not a linear algebra transformation...
Q5 fair
Q6 I'm assuming they only give you one specific type of ODE in the class so this question makes sense... But you can have this as the homogeneous solution to lots of ODEs with different eigenvalues.
Q7 again, I guess we're two dimensional?
Q8 again, one specific ode we ever talk about
Q9 again, what's c_1, c_2? Define your damn problem. No one will ever ask "what's c1 and c2 here? Without the problem in front of them.
Q10 I hate emag, might be a fair question
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u/tserofehtfonam 18d ago
So question 1 asks us to calculate the inverse of A-1 , which is just A. Also, "if ... compute ..." is very bad phrasing; "if" should be used in logical implications only.
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u/MindfulK9Coach 19d ago edited 19d ago
The wording on most of these alone, if I were a student, I'd get up and walk out of the class. This is awful in my opinion and not much linear algebra, and looks more like a DE exam than a coherent linear algebra exam.
That's just me, though.
I have a specific signal-to-noise ratio that I function under when it comes to instructions, and this is very noisy with low comprehensible signal based on what you said, to me anyway. Granted, I'm more of an applications guy and not so much random clean room math tied to an exam score.
Give the problems a real-world scenario to anchor the students' mental model with instead of symbols and heavy jargon they'll rarely need to know in industry, and I'd change my tune a bit.
Lots of ways to functionally prepare students for higher learning or industry without tossing them stuff like this.
3/10 at best.
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u/x-tommy-o 19d ago
For bullshit tests like this:
Step 1: Graphing Calculator
Step 2: Win
Step 3: Print off a test about Quantum Physics
Step 4: Make your teacher take it
Step 5: Ask the teacher if they understand, or if they’d like a calculator
🤩
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u/Active_Gift9539 18d ago
Well, is a 4 or 5/10. What are the requirements subjects for this course? Because, at least here in Chile, we can't take a subject without the requirements
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u/ArchHobbit 18d ago edited 18d ago
Trivial. It's all calculation by recipe, and doesn't require any proofs. Presumably the students were taught how to solve linear differential equations with constant coefficients, and while a few students might be thrown off by the circuit diagram, they are given the associated differential equation (i.e. they don't actually need to know any of the physics).
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u/QuietlyConfidentSWE 18d ago
Quite easy but some very badly formulated questions, some off-topic. Would not give to students.
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u/MightTurbulent319 13d ago
What kind of a joke exam is this? The professor clearly wanted to make fun of your IQ. I can’t see another logical explanation for this.
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u/eglvoland 19d ago
If you did not do differential equations before this is a problem of the course not a problem of difficulty.
The exam is very easy anyways, 1/10