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.

Àwọn ààtò àwọn ìṣàmúlò-ètò · [[3],[4]]

Linear-Algebra · Matrices

[[3],[4]]

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

Àwọn ìṣàmúlò-ètò

\left[\begin{matrix}3\\4\end{matrix}\right]
A 2×1 matrix.
\operatorname{rank} A = 1
Rank (number of independent rows).
A^T = \left[\begin{matrix}3 & 4\end{matrix}\right]
Transpose.

Fi àwọn àgbèwọlé hàn

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

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Bii o ṣe le: Vectors

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

Àwọn Àtòjọ-ẹ̀yàn

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.

Diẹ̀ nínú Precalculus

Complex numbers Polynomial functions Rational functions Sequences and series The binomial theorem Conic sections Exponential and logarithmic functions Polynomial division and the remainder theorem Parametric equations and polar coordinates