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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Consider an matrix A and a nonzero vector of length . If multiplying A with (denoted by ) simply scales by a factor of λ, where λ is a scalar, then is called an eigenvector of A, and λ is the corresponding eigenvalue.
Months after its $80 million Series B fundraise, Course Hero has acquired Symbolab, an artificial intelligence-powered calculator that helps students answer and understand complex math questions.
Since x 2 represents the area of a square with side of length x, and bx represents the area of a rectangle with sides b and x, the process of completing the square can be viewed as visual manipulation of rectangles. Simple attempts to combine the x 2 and the bx rectangles into a larger square result in a missing corner.
Unlike rectangular differential volume element's volume, this differential volume element's volume is not a constant, and varies with coordinates (ρ and φ). It can be used to transform integrals between the two coordinate systems:
Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...
The rectangular region at the bottom of the body is the domain of integration, while the surface is the graph of the two-variable function to be integrated. In mathematics (specifically multivariable calculus ), a multiple integral is a definite integral of a function of several real variables , for instance, f ( x , y ) or f ( x , y , z ) .
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain.In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1]