Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem is to solve the system of two linear equations with two variables: $x + y = 9$ $2x + 3y ...

Linear EquationsSystems of EquationsSubstitution Method
2025/5/9

The problem is to factor the quadratic expression $x^2 + 2x - 15$.

Quadratic EquationsFactoringPolynomials
2025/5/9

The problem asks us to find the value of $x$ given the matrix equation: $$ \begin{bmatrix} 6 & -2 \\...

Linear AlgebraMatrix OperationsMatrix MultiplicationSolving Equations
2025/5/9

The problem asks us to find the value of $x$ given the matrix equation $\begin{bmatrix} 9 & 4 \\ -3 ...

Linear AlgebraMatrix EquationsMatrix MultiplicationSystems of Equations
2025/5/9

We are given a matrix equation: $[4 \ 3] \begin{bmatrix} 1 & -2m \\ 3 & -1 \end{bmatrix} = [13 \ -35...

Matrix AlgebraMatrix EquationsLinear Equations
2025/5/9

We are asked to solve two complex number problems: (e) Simplify $\frac{1}{(2+i)(\sqrt{3}-2i)}$ (f) S...

Complex NumbersComplex Number ArithmeticSimplificationRationalization
2025/5/9

The problem requires us to multiply a $2 \times 1$ matrix with a $2 \times 2$ matrix: $\begin{bmatri...

Matrix MultiplicationLinear AlgebraMatrix Operations
2025/5/9

We are asked to simplify expressions involving square roots of negative numbers and express the resu...

Complex NumbersSimplificationSquare Roots
2025/5/9

The problem gives a matrix equation and asks us to find the values of $p$ and $q$. The equation is: ...

MatricesMatrix EquationsLinear AlgebraScalar MultiplicationMatrix Subtraction
2025/5/9

We are given the following matrix equation: $ \begin{bmatrix} 4 & -2 \\ 3 & -6 \end{bmatrix} \begin{...

MatricesMatrix MultiplicationLinear EquationsProblem Analysis
2025/5/9