Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are given two matrices, $A = \begin{bmatrix} 1 & 3 & 0 \\ 5 & 4 & 3 \\ 0 & 3 & 2 \end{bmatrix}$ a...
Matrix MultiplicationTransposeLinear Algebra
2025/3/8
We are given two matrices $A$ and $B$, where $A = \begin{bmatrix} 2 & 1 & 0 \\ 7 & 2 & 8 \\ 1 & 0 & ...
MatricesMatrix MultiplicationLinear Algebra
2025/3/8
We are given two matrices, $A$ and $B$, and we need to find the matrix product $BA$. The matrix $A$ ...
Matrix MultiplicationLinear Algebra
2025/3/8
We are given two matrices, $D = \begin{bmatrix} 2 & 6 \\ 7 & 3 \end{bmatrix}$ and $E = \begin{bmatri...
MatricesMatrix Multiplication
2025/3/8
The problem asks to find the inverse element for the operation $*$ defined as $x * y = \frac{2x + 2y...
Abstract AlgebraInverse ElementIdentity ElementBinary Operation
2025/3/8
We are asked to simplify the expression $\frac{a^{\frac{1}{2}} \times a^{\frac{1}{4}}}{a}$.
ExponentsSimplificationFractionsAlgebraic Expressions
2025/3/8
Simplify the expression $\sqrt[3]{a^2} \times \sqrt{a^{-3}}$.
ExponentsRadicalsSimplificationFractional Exponents
2025/3/8
The problem is to evaluate the expression $(\frac{1}{32})^{\frac{-4}{3}}$.
ExponentsRadicalsSimplification
2025/3/8
The problem is to simplify the expression $1 \div 2 \cdot \sqrt{x^{-3}}$.
SimplificationRadicalsExponentsRationalization
2025/3/8
The problem is to simplify the expression $\frac{1}{2\sqrt{x^{-8}}}$.
SimplificationExponentsRadicals
2025/3/8