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HomeHomework HelpmathematicsFundamental Theorem of Algebra and Matrix Addition

Fundamental Theorem of Algebra and Matrix Addition

The Fundamental Theorem of Algebra states that every non-constant polynomial has at least one complex root, and matrix addition is defined by combining corresponding entries of two matrices of the same size.

intermediate
3 hours
Mathematics
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Overview

The Fundamental Theorem of Algebra is a key principle in mathematics that guarantees the existence of roots for polynomial equations, extending our understanding of numbers to the complex plane. This theorem is foundational for higher-level mathematics and applications in various fields such as engi...

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Key Terms

Polynomial
An expression consisting of variables and coefficients.

Example: f(x) = 2x² + 3x + 1

Complex Number
A number that has a real part and an imaginary part.

Example: 3 + 4i

Root
A solution to the equation f(x) = 0.

Example: x = 2 is a root of x² - 4 = 0

Matrix
A rectangular array of numbers arranged in rows and columns.

Example: [[1, 2], [3, 4]]

Element-wise Addition
Adding corresponding elements of two matrices.

Example: If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A + B = [[6, 8], [10, 12]]

Degree of Polynomial
The highest power of the variable in a polynomial.

Example: In 2x³ + 3x², the degree is 3.

Related Topics

Linear Equations
Study of equations that graph as straight lines, foundational for understanding matrices.
intermediate
Vector Spaces
Explores collections of vectors and their properties, closely related to matrices.
advanced
Eigenvalues and Eigenvectors
Important concepts in linear algebra that relate to matrix transformations.
advanced

Key Concepts

Complex RootsPolynomial EquationsMatrix OperationsLinear Algebra