How to tell if a columns of matrix are linear dependent?
How can it be seen if the following matrix is linear dependent? Let $A= \begin{bmatrix} 0 & -3 & 9& \\ 2&1& 7 \\ -1& 4 &-5 \\ ...
19 Apr 2026 1 READS
Archive: General
Check existence of cycle in graph with only number of vertices and their degree
I know that we can check existence of cycle in graph by simply traversing the graph and check whether the vertex has been visited. However, if there are o...
19 Apr 2026 1 READS
How to find the coordinate vector x with respect to the basis B for R^3?
Find the coordinate vector of $x = \begin{bmatrix}-5\\-2\\0\end{bmatrix}$ with respect to the basis $B = \{ \begin{bmatrix}1\\5\\2\end{bmatrix}, \begin{bm...
19 Apr 2026 1 READS
Elementary proof that the MacLaurin series of $\sin x$ converges to $\sin x$ for all $x$
In my book it is given: $\sin x = x- \dfrac {x^3}{3!}+\dfrac{x^5}{5!}- \dfrac{x^7}{7!}...$ I googled around for a proof but couldn't understand any o...
19 Apr 2026 1 READS
Which positive whole number below 100 has the most number of factors?
Is there a mathematical function that can be done without a computer that accurately outputs the number of factors a number has, then solve this problem? ...
19 Apr 2026 1 READS
Calc 3, finding planes that are parallel and perpendicular.
So I really need help with figuring out how to do this problem. I answered two of the questions (not sure if I am right) and I am just stuck on the 2nd pa...
19 Apr 2026 1 READS
Square units of area in a circle
I'm studying for the GRE and came across the practice question quoted below. I'm having a hard time understanding the meaning of the words they&...
19 Apr 2026 1 READS
Construct a polynomial function with the given graph
Where does one begin? I can see that the zeros are -5, -3, 0, and 4? Is that correct so far?
19 Apr 2026 1 READS
Solve $100n^2 = 2^n$
I don't understand how to solve this... I try to get rid of the $2^n$ via logarithms and it leads me to $2log_210 + 2log_2n = n$ and I don't kno...
19 Apr 2026 1 READS
Find the coefficient of $x^{70}$ in $(x^1-1)(x^2-2)(x^3-3)\cdots(x^{12}-12)$.
Find the coefficient of $x^{70}$ in $(x^1-1)(x^2-2)(x^3-3)\cdots (x^{12}-12)$. I tried to solve this problem using theory of equation the coefficient of $...
19 Apr 2026 1 READS
