I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of ma...

I need to show that $\text{Adj}(AB) = \text{Adj}(B)\text{Adj}(A)$, where $A$ is an $N$x$M$ matrix, and $B$ is an $M$x$K$ matrix, and $\text{Adj}(A)$ denot...

Given two circles $x^2+(y-4)^2=4^2$ and $(x-8)^2+(y+2)^2=2^2$ I need to find the circle that's orthogonal to both the above circles, and contains the...

What is indefinite integral? This is the question that always perplexes me. First my book wrote that Indefinite integral of $f(x)$ is $F(x)$ if on differe...

Find all positive inegers solution for the following diophantine equation $$x^2-xy-y^2=1$$ My work so far 1)$$x^2-xy-y^2-1=0$$ $$D=y^2+4(y^2+1)=5y^2+4=k^2...

I have this thorem in my book, H', denotes the dual space, that is the set of bounded linear operators from X to the field over X. The way they got t...

prove that there is some number x such that $ x^{179}+\frac{163}{1+x^2+\sin^2x}=119$ I really want to know the general process to prove something like tha...

I want to proof that $S_n$ is generated by the set of transpositions ${(1,2),(1,3), \ldots , (1,n)}$ using that $(k,j) = (1,k)(1,j)(1,j)$ but I don't...

For: -10 mod 7 I know the answer is 4, but how do you actually get to the answer by hand?

I'm talking about the row echelon form, not the reduced row echelon form. If it isn't can you give me some examples?