MethodMath Math Questions and Answers

I'm studying linear algebra and I need to solve systems of equations using Gaussian elimination. For example:

I know I need to form an augmented matrix and use row

I'm studying linear algebra and I need to understand how to compute the rank of a matrix. I know the definition:

The rank of a matrix is the dimension of

I need to integrate $\int \frac{x^2 + 2x + 3}{(x-1)(x+2)^2} \, dx$ and I know I need partial fractions first.

The general decomposition is:

But I always make mistakes solving for $A$, $B$, and

This problem is all over Twitter and Instagram right now:

A square is inscribed in a semicircle of radius $R$. Find the area of the square in terms of

In school they told us "you cant divide by zero" but they never explained WHY.

Like if you divide a number by a really small number you get a really

This is an IIT-JEE problem that has been bothering me:

Find the number of solutions to the equation $\sin x = \frac{x}{10}$ for $x \in \mathbb{R}$.

I tried solving it analytically but it seems

I am studying probability theory and I need to understand moment generating functions (MGFs). The MGF of a random variable $X$ is:

My questions:

1. Why is it called

I'm studying combinatorics and I'm stuck on a problem involving permutations with restrictions.

Problem: \"How many ways can 5 distinct mathematics books and 3 distinct physics books be arranged on