Guest wrote:Hello everybody
I would like to ask for help for my girlfriend. She is struggling with a math homework and it's been a long time since I had math lessons, so I can not help her. Her teacher is quite bad - he left these topics on self-studing and she has no idea
. Can you help her with solving these problems? This homework is important for passing
No matter how "bad" her teacher is, hasn't your girlfriend at least read the textbook? The first problem asks her to solve a system of equations. That's typically learned in a basic algebra course and expanded on in "Linear Algebra".
The second problem ask for values of "a" so that the system of equations has "one" or "none" or "infinitely many" solutions. So try to solve
the system. What might happen so that it can't be solved? Most likely there will come a time when you have to divide by something involving "a". If that is equal to 0, either of two things can happen: (i) you are trying to divide a non-zero number in which case there is no solution or (ii) you are dividing "0/0" in which case there are a infinite number of solutions
The third problem shows four "homogenous" systems of equations that have the "trivial solution" and asks which also have non-trivial solutions. Does your girlfriend know what "trivial" and "non-trivial" solutions are? (a) has three equations in four unknowns and (c) has two equations in three unknowns. What does your girlfriend think of that? (g) can be solved "by sight". The last equation is "[tex]5x_3= 0[/tex]". So what
must [tex]x_3[/tex] be? And what does the second equation become when you replace [tex]x_3[/tex] with that?
The fourth problem asks for a solution "by Cramer's rule". Does your girl friend know what that is?
by Guest » Mon Oct 15, 2018 12:51 pm 
529060207_linearalgebra_hw.f18-1.pdf
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