“How can we represent a set of vectors?”
Vectors are one of the most important aspects of Linear Algebra. But in order to have a true set of vectors, they must be closed under vector addition and scalar multiplication. This is known as a Vector Space and is vital for a true understanding of Linear Algebra.
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Block Diagrams for Controls Systems
“How can we represent control process graphically?”
Control systems are a bedrock of modern day technology. However, sometimes it would be easier to see their processes if visualized. This can be done by using Block Diagrams, which shows each component of the control system in its natural order.
“How can we flip rows and columns of a matrix?”
When doing Linear Algebra, there are times where we may want to flip the rows and columns. This can be accomplished through Matrix Transposition. A matrix that has undergone transposition is known as a transposed matrix. If we multiply the transposed matrix by the original matrix then we arrive at the identity matrix.
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The Span of a Matrix
“How can we represent all possible combinations of a matrix?”
Matrices are great for representing groups of numbers. But sometimes we would like to see all possible results. We can do this using the Span of a Matrix, using weighted values for each part.
“What happens when we have a matrix where everything outside of the diagonal is zero?”
Matrices come in all shapes and sizes. But some of them are very special indeed. One of these include matrices where everything outside of the main diagonal is zero. These very special easy to solve matrices are known as Diagonal Matrices and are great for solving equations.
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The Difference Between Probability and Statistics
“What is the difference between Probability and Statistics?”
In everyday talk, probability and statistics are lumped together. But in reality they are more like two sides of the same coin. Probability is the prediction of the likelihood of future events while Statistics is the analysis of the frequency of past events. Therefore, this is The Difference Between Probability and Statistics.
Why Planar Lines With the Same Slope Never Meet
“Why is is that lines in a plane with the same slope never meet?”
Lines in a plane usually intersect at some point. But with one exception. If the lines have the same slope, then they will never meet! This is because they are parallel to each other and planar parallel lines never meet.