Understanding Vectors in Mathematics

An agent that carries and transmits an infectious pathogen into another living organism.

A small piece of DNA into which a foreign DNA fragment can be inserted for cloning purposes.

An n-dimensional vector of numerical features that represent some object.

<p>A display device used for early computers.</p> Signup and view all the answers

<p>A tool commonly used by molecular biologists to deliver genetic materials into cells.</p> Signup and view all the answers

<p>Linear algebra is the branch of mathematics that deals with linear equations, linear maps, vector spaces, and matrices. It is essential for various areas of mathematics, as well as sciences and engineering.</p> Signup and view all the answers

<p>Linear algebra is fundamental in modern presentations of geometry, functional analysis, and modeling natural phenomena in sciences and engineering. It is also used for dealing with first-order approximations for nonlinear systems.</p> Signup and view all the answers

<p>Linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes, and rotations.</p> Signup and view all the answers

<p>The procedure for solving simultaneous linear equations, known as Gaussian elimination, appeared in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.</p> Signup and view all the answers

<p>Functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to function spaces.</p> Signup and view all the answers

<p>Linear algebra is used in modeling many natural phenomena and computing efficiently with such models because it allows for the representation of systems of linear equations and operations with matrices, which are essential for these purposes.</p> Signup and view all the answers

<p>The procedure for solving simultaneous linear equations, now called Gaussian elimination, appeared in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.</p> Signup and view all the answers

<p>Linear algebra is fundamental in modern presentations of geometry as it is used for defining basic objects such as lines, planes, and rotations, and for performing transformations and operations in geometric spaces.</p> Signup and view all the answers

<p>Functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to function spaces, allowing for the study and analysis of functions and their properties.</p> Signup and view all the answers

<p>Linear algebra is used in almost all areas of mathematics, in sciences, and in fields of engineering for modeling natural phenomena, computing efficiently, and for dealing with first-order approximations of nonlinear systems.</p> Signup and view all the answers