Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
Let $A: R^2 \to R^2$ be a linear operator. Its matrix representation in the standard basis $(e_1, e_...
Linear TransformationsChange of BasisMatrix RepresentationEigenvalues and Eigenvectors
2025/5/14
We need to compute the element $a_{11}$ of the matrix $A = (Q^T Q)^3$, where $Q = \begin{pmatrix} 0 ...
Matrix MultiplicationMatrix TransposeMatrix PowersIdentity Matrix
2025/5/14
The problem asks to find the domain and range of the function $f(x) = \frac{1}{x}$.
FunctionsDomainRangeRational Functions
2025/5/14
The problem asks us to evaluate the function $g(x) = -2|4x - 8| + 3$ at $x = -4$. This means we need...
Absolute ValueFunction EvaluationAlgebraic Manipulation
2025/5/14
The problem is about complex numbers. a. Given $z_1 = \sqrt{2} + i\sqrt{2}$, find $\overline{z_1}$ (...
Complex NumbersComplex ConjugateModulusArgumentTrigonometric FormRoots of Equations
2025/5/14
The problem asks us to match the given inequalities with their corresponding number line representat...
InequalitiesSolving InequalitiesNumber Lines
2025/5/14
The problem asks us to draw the graph of the equation $y = 4x - 2$ on the given grid.
Linear EquationsGraphingSlope-intercept formCoordinate Geometry
2025/5/14
The problem asks us to draw the graph of the equation $y = -x + 6$ on the given grid.
Linear EquationsGraphingSlope-intercept form
2025/5/14
The problem requires us to factor linear expressions and fill in the blanks to complete the factored...
FactoringLinear ExpressionsGreatest Common Factor (GCF)
2025/5/14
The problem asks to determine the gradient, y-intercept, and the equation of the graph for each of t...
Linear EquationsSlopeY-interceptCoordinate Geometry
2025/5/14