InsightCalc
Step-by-Step Problems
Linear Algebra
Problems related to linear algebra, including systems of equations and matrix operations.
(457077000)(abc)=(9810)\begin{pmatrix}4 & 5 & 7\\ 0 & 7 & 7\\ 0 & 0 & 0\end{pmatrix}\begin{pmatrix}a\\ b\\ c\end{pmatrix}=\begin{pmatrix}9\\ 8\\ 10\end{pmatrix}
#Linear algebra#Matrix
System of Linear Equations in Matrix Form
Solve systems of linear equations represented in matrix form. A system of equations can be written as Ax=B\mathbf{A}\mathbf{x} = \mathbf{B}, where all the numbers line up neatly in matrices. This makes it easier to solve many equations at once, see if solutions exist, and use methods like elimination or inverses without writing everything out by hand.
(8410711276)(abc)=(841)\begin{pmatrix}8 & 4 & 1\\ 0 & 7 & 11\\ 2 & 7 & 6\end{pmatrix}\begin{pmatrix}a\\ b\\ c\end{pmatrix}=\begin{pmatrix}8\\ 4\\ 1\end{pmatrix}
Determinant
Calculate the determinant of a given matrix with steps. The determinant is a special number you get from a square matrix. It’s super useful for checking if a matrix can be inverted, solving systems of equations, and understanding properties like area, volume, or transformations.
det⁡(457877123−8)\det \begin{pmatrix}4 & 5 & 7\\ 8 & 7 & 7\\ 12 & 3 & -8\end{pmatrix}
Derivative
Finds derivative of a function with steps. The derivative shows how fast a function is changing at any point. It’s key for finding slopes, optimization, and understanding motion or growth in real problems.
derivative x4+5x3+2derivative\:x^4+5x^3+2derivative arccos⁡(x2)derivative\:\arccos(x^2)derivative (x+6)(x−2)⋅sin⁡(x)derivative\:(x+6)(x-2)\cdot\sin(x)
Linear Equation
Solve linear equations of the form ax + b = 0. Useful for basic algebra and introductory problem solving.
(x+6)(x−4)−x2=4x+5(x + 6)(x - 4) -x^2=4x+54−x2=3x−2\frac{4-x}{2}=3x-2
Quadratic Equation
Solve quadratic equations of the form ax^2 + bx + c = 0, including step-by-step solutions and explanations.
x2−7x+8=0x^2-7x+8=0x2−4=10xx^2-4=10x
Eigenvalues
Calculate the eigenvalues of a matrix. Eigenvalues are important in linear algebra, physics, and engineering for understanding matrix properties and transformations.
eigenvalues (1−1120−23−1−1)eigenvalues\:\begin{pmatrix}1 & -1 & 1\\ 2 & 0 & -2\\ 3 & -1 & -1\end{pmatrix}