Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are given the following matrix equation: $ \begin{bmatrix} 4 & -2 \\ 3 & -6 \end{bmatrix} \begin{...
MatricesMatrix MultiplicationLinear EquationsProblem Analysis
2025/5/9
The problem gives two matrices, $P = \begin{bmatrix} 2 & 5 \\ -4 & 6 \end{bmatrix}$ and $Q = \begin{...
Matrix OperationsMatrix SubtractionScalar Multiplication
2025/5/9
We are given a matrix equation $[2p \quad 3]\begin{bmatrix} 4 \\ -6 \end{bmatrix} = [6]$ and need to...
Matrix AlgebraLinear EquationsSolving Equations
2025/5/9
We are given a matrix equation: $\begin{bmatrix} 3 \\ -2 \\ 5 \end{bmatrix} - F + \begin{bmatrix} -4...
Matrix AlgebraMatrix OperationsLinear AlgebraMatrix Equations
2025/5/9
The problem requires us to find the matrix $M$ given the equation: $ \begin{bmatrix} 6 \\ -7 \end{bm...
Linear AlgebraMatrix OperationsMatrix AdditionScalar Multiplication of Matrices
2025/5/9
The problem requires us to solve for $p$, $q$, and $r$ given the matrix equation: $\begin{bmatrix} p...
MatricesMatrix MultiplicationLinear Equations
2025/5/9
The problem consists of three parts: (i) Determine if the function $f(x) = x^2$ is odd or even. (ii)...
FunctionsEven and Odd FunctionsComplex NumbersDifferentiationCalculusFirst Principles
2025/5/8
The problem has three parts: (i) Simplify the expression $(4\sqrt{2} + \sqrt{3})(3\sqrt{2} + 2\sqrt{...
SimplificationDerivativesCalculusPolynomial EquationsRational Root Theorem
2025/5/8
The problem consists of three parts: (i) Differentiate $y = (3x+1)^3$ with respect to $x$. (ii) Give...
DifferentiationChain RuleFunction CompositionRationalizationConjugates
2025/5/8
The problem consists of three parts: (i) Given two sets $A = \{1,2,3,4,5,6,7,8,9,10\}$ and $B = \{2,...
Set TheoryPolynomial DivisionSimplificationRadicals
2025/5/8