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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.
Ohatra · [[3],[4]]
Dingana amin'ny dingana
- \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.
Asehoy ny valinteny
Ankehitriny ianao Misafidiana olana iray, na soraty na esory ny anao manokana. Ny dingana tsirairay, sary iray, ny valiny miafina mandra-pahafantaranao.
Ny kaonty maimaimpoana dia mampiditra ny fanamarihana amin'ny lesona tsirairay, ny tahirin'ny zavatra vitanao, ny olana voavahao ao amin'ny toerana iray, ary ny mpampianatra iray izay azonao anontanio momba ity pejy ity. misokatra ho an'ny rehetra ny matematika, na efa niditra na tsy niditra.
Misoratra anarana FidiranaMarika ampiasaina eto
Tsindrio ny marika iray mba hahitana ny famaritana feno, sary, ary ny dikan'ny litera tsirairay ao aminy.
Ahoana ny fomba: Vectors
- A 2×1 matrix.
- Rank (number of independent rows).
- Transpose.
Fanontaniana napetrak'ireo olona
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.
Mbola maro ao Precalculus
Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremConic sectionsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates