maths.free › Precalculus › Vectors

Vectors

Magnitude, direction, components, and adding vectors head to tail.

A vector is a quantity with magnitude and direction, displacement, velocity, force. In components it is just a column of numbers, adding entry by entry; its length comes from Pythagoras. Linear algebra picks up here.

Ýüklenen mysal · [[3],[4]]

Linear-Algebra · Matrices

[[3],[4]]

\left[\begin{matrix}3\\4\end{matrix}\right]

Adım adım

  1. \left[\begin{matrix}3\\4\end{matrix}\right]

    A 2×1 matrix.

  2. \operatorname{rank} A = 1

    Rank (number of independent rows).

  3. A^T = \left[\begin{matrix}3 & 4\end{matrix}\right]

    Transpose.

Jawaby görkez
\left[\begin{matrix}3\\4\end{matrix}\right]

Indi sen Bir meseläni saýla, ýa-da ýaz ýa-da özüňi surata çek. Her ädim, bir resim, jogap sorag berlençä gizlenýär.

Özüň işle

Mugt hasap her bir ders üçin notlar goşýar, tamamlanan zadyňyzyň ýazgysyny, çözen problemaňyzy bir ýerde, we bu sahypa barada sorap biljek mugallymy. Matematika özüçe her kim üçin açyk, girseň ýa girmeseň.

_Gün _Giriş

Şu ýerde ulanylan simwollar

Eň täze düşündirme, surat, we her harpyň manysy üçin her bir simwoly basyň.

Nädip: Vectors

  1. A 2×1 matrix.
  2. Rank (number of independent rows).
  3. Transpose.

Adamlar soraýan soraglar

What is a function, really?

A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.

Why do we need complex numbers?

Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.

_Ýaşa Precalculus

Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremConic sectionsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates