vector algebra Archives - Infinity is Really Big

July 1, 2019September 20, 2019

High-Dimensional Linear Algebra

Visual Linear Algebra Online, Section 1.7

Image by Danilo Bueno from Pixabay

Many practical situations that require the use of linear algebra can involve hundreds or even thousands of unknowns. Modeling a national economy, optimizing the purchase of supplies, and managing flight schedules are prominent examples.

A vector quantity representing all the data in such a situation might therefore … Read the rest

June 25, 2019September 12, 2019

Linear Algebra in Three Dimensions

Visual Linear Algebra Online, Section 1.6

The solution set of a certain system of three linear equations and three unknowns is the line of intersection of three planes. ‘Typically’, three planes will intersect at just one point, however.

Linear algebra has immense practical value in our modern world. Statistics, business, science, and engineering all make heavy use of the

… Read the rest

May 30, 2019September 5, 2019

Systems of Linear Equations in Two Dimensions

Visual Linear Algebra Online, Section 1.3

Visualizing the parametric vector form of the solution set of a system with infinitely many solutions.

Jack and Jill earn a combined $79.50 when Jack works 2 hours and Jill works 3 hours. On the other hand, if Jack works 3 hours and Jill works 2 hours, they make $78.75 total. What are

… Read the rest

May 21, 2019September 5, 2019

Vectors in Two Dimensions

Visual Linear Algebra Online, Section 1.2

Image by Keith Johnston from Pixabay

A big-league baseball player smashes a four-seam fastball with the sweet-spot of the bat. Is it a home run? The answer is — it depends. It depends on the launch angle and on it being a “fair ball”. In other words, what is the

… Read the rest