linearalgebra.cs.umanitoba.ca

Linear Algebra Wiki - Linear Algebra

Vectors in $ R 2$ and $ R 3$. Review of coordinates and graphs of functions in $ R 2$. The real line $ R$. Distance between points in $ R$. Addition and multiplication in $ R$. The Cartesian plane, or $ R 2$. Distance between points in $ R 2$. Graphs in $ R 2$. Graphs of functions in $ R 2$. Addition and scalar multiplication of vectors in $ R 2$. Scalar Multiplication in $ R 2$. Geometric interpretation of scalar multiplication in $ R 2$. Addition in $ R 2$. Geometric interpretation of addition in $ R 2$.

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Linear Algebra Wiki - Linear Algebra | linearalgebra.cs.umanitoba.ca Reviews

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Vectors in $ R 2$ and $ R 3$. Review of coordinates and graphs of functions in $ R 2$. The real line $ R$. Distance between points in $ R$. Addition and multiplication in $ R$. The Cartesian plane, or $ R 2$. Distance between points in $ R 2$. Graphs in $ R 2$. Graphs of functions in $ R 2$. Addition and scalar multiplication of vectors in $ R 2$. Scalar Multiplication in $ R 2$. Geometric interpretation of scalar multiplication in $ R 2$. Addition in $ R 2$. Geometric interpretation of addition in $ R 2$.

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3 jump to navigation

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5 point slope form

6 slope intercept form

7 parametric form

8 coordinate form

9 displacement form

10 angle between vectors

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Linear Algebra Wiki - Linear Algebra | linearalgebra.cs.umanitoba.ca Reviews

https://linearalgebra.cs.umanitoba.ca

Vectors in $ R 2$ and $ R 3$. Review of coordinates and graphs of functions in $ R 2$. The real line $ R$. Distance between points in $ R$. Addition and multiplication in $ R$. The Cartesian plane, or $ R 2$. Distance between points in $ R 2$. Graphs in $ R 2$. Graphs of functions in $ R 2$. Addition and scalar multiplication of vectors in $ R 2$. Scalar Multiplication in $ R 2$. Geometric interpretation of scalar multiplication in $ R 2$. Addition in $ R 2$. Geometric interpretation of addition in $ R 2$.

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linearalgebra.cs.umanitoba.ca

1

The Cartesian plane - Linear Algebra

http://linearalgebra.cs.umanitoba.ca/linearalgebra/index.php/The_Cartesian_plane

The Cartesian Plane, or $ R 2$. To form the Cartesian plane, take two copies of the real line, one horizontal and one vertical, and place them so that they cross at the zero points on both lines. The horizontal line is called the $x$-axis. And the vertical line is called the $y$-axis. They look like this:. Of the point, and the pair $(x,y)$ is called the coordinates of the point. The four points $(2,4)$, $(-1,-2)$, $(-1.5,2.75)$ and $( sqrt2,- pi)$. Determining the point with coordinates $(x 0,y 0)$.

2

Addition and scalar multiplication of vectors in R2 - Linear Algebra

http://linearalgebra.cs.umanitoba.ca/linearalgebra/index.php/Addition_and_scalar_multiplication_of_vectors_in_R2

Addition and scalar multiplication of vectors in R2. The points in $ R 2$ are also called vectors. And the real numbers are also called scalars. The product of a scalar and a vector is defined so that the product is a vector. The process is called scalar multiplication. Definition of Scalar Multiplication in $ R 2$. Examples of scalar multiplication. Theorem (Geometry of scalar multiplication). Definition of Addition in $ R 2$. A construction: completing the parallelogram. Pi(-2,4)=(-2 pi,4 pi)$. For any...

3

Vectors in R2 - Linear Algebra

http://linearalgebra.cs.umanitoba.ca/linearalgebra/index.php/Vectors_in_R2

We may consider the vectors in $ R 2$ to simply be the usual points in the plane which we described in great detail here. We can view addition geometrically using the parallelogram rule:. We can also view scalar multiplication geometrically by stretching or shrinking the vector ( mathbf x ):. Retrieved from " http:/ linearalgebra.cs.umanitoba.ca/linearalgebra/index.php/Vectors in R2. Log in / create account. This page was last modified on 4 March 2013, at 18:27. This page has been accessed 478 times.

4

Equations of lines in R2 - Linear Algebra

http://linearalgebra.cs.umanitoba.ca/linearalgebra/index.php/Equations_of_lines_in_R2

Equations of lines in R2. We know how to describe all the points on the line joining $ mathbf0$ to a point $ mathbf v not= mathbf0$. It consists of all points of the form $t mathbf v$ where $t$ is a real number. This means that if $ mathbf v=(a,b)$, then any point on the line joining $ mathbf v$ to $ mathbf0$ is of the form $t(a,b)=(ta,tb)$. What happens if $a=0$? Theorem (Equation of a line in $ R 2$ through $ mathbf0$). Theorem (Equation of a line joining two points). Theorem (Parametric form of a line).

5

Combining addition and scalar multiplication - Linear Algebra

http://linearalgebra.cs.umanitoba.ca/linearalgebra/index.php/Combining_addition_and_scalar_multiplication

Combining addition and scalar multiplication. Sometimes both addition and scalar multiplication are used in several steps to evaluate expressions. For example, if $ mathbf v=(1,3)$, $ mathbf w=(2,1)$, $r=2$ and $s=3$, then [ r mathbf v s mathbf w = 2(1,3) 3(2,1)=(2,6) (6,3)=(8,9) ] This also makes sense geometrically. Adding more that two terms also makes sense: if $ mathbf v=(4,1)$, $ mathbf w=(-1,-1)$, $ mathbf x=(0,1)$, $r=-1$, $s=3$, and $t=-4$, then. Log in / create account.

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linearalgebra.cs.umanitoba.ca

Linear Algebra Wiki - Linear Algebra

Vectors in $ R 2$ and $ R 3$. Review of coordinates and graphs of functions in $ R 2$. The real line $ R$. Distance between points in $ R$. Addition and multiplication in $ R$. The Cartesian plane, or $ R 2$. Distance between points in $ R 2$. Graphs in $ R 2$. Graphs of functions in $ R 2$. Addition and scalar multiplication of vectors in $ R 2$. Scalar Multiplication in $ R 2$. Geometric interpretation of scalar multiplication in $ R 2$. Addition in $ R 2$. Geometric interpretation of addition in $ R 2$.

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