$A =\left(\begin{array}{ccc} 0 & 1 & b \\ -1 & 0 & c \\ -b & -c & 0 \end{array}\right)$ I tried to come up with the RREF($A$), but...

To explain my question, here is an example. Below is an AP: 2, 6, 10, 14....n Calculating the nth term in this sequence is easy because we have a formula....

Taking the angle at center as $x$, I got $r \sin x =2$. But after that how to proceed?

What is wrong with this solution of Solve for $ (2x)^{\ln2 }= (3y)^{\ln3 }$ $3^{\ln x} = 2^{\ln y} $ Here is my solution- $ (2x)^{\ln2 }= (3y)^{\ln3 }$ $ ...

Sard's Theorem: Suppose $M$ and $N$ are smooth manifolds with or without boundary and $F:M\to N$ is a smooth map. Then the set of critical values of ...

The associative law of multiplication for three positive integers $a,b$ and $c$ can be proved$^1$ from the Commutative Law and the property of "Number of ...

I am starting to study linear algebra, and a problem appeared at the beginning of the textbook, the problem is the following: What 3-vector u satisfies $(...

The fundamental group of the torus is isomorphic to $\mathbb{Z}\oplus\mathbb{Z}$. I know that the $\oplus$ symbol is the exclusive or symbol but I don...

I have the problem: Decompose the vector $\vec v = (1,2,4)$ in two parts, one parallel to the plane $X = (1,1,0) + \lambda(1,0,1) + \gamma(0,1,-1)$ and ot...

I need to prove that $0*a = a*0 = 0$ using only axiomatic properties for real numbers(It's a exercise from Apostol's book. My try: We can write ...