Example of matrix column vector multiplication via linear combinations

We explore matrix-column-vector multiplication

00:00 -Introduction
00:12 -Useful habit: Analyze the dimensions
00:35 -The inner dimensions must agree
00:48 -The size of the product is defined by the outer dimensions
01:11 -Strengthen your memory via active recall
01:35 -Review the formal definition
01:45 -Great habit: translate notation of definition into notation of problem
02:23 -Apply the definition to the example problem
03:05 -The modeling matrix and the algebraic worker
03:30 -Major idea of using linear algebra for mathematical modeling
04:15 -When modeling matrix is on left, we partition into columns
04:35 -Unroll the sum to get all terms in the linear combination
05:15 -Substitute the individual entries from this example
06:03 -Do all the scalar vector multiplications
06:45 -Timed tests are silly: Math is about slow, deep, deliberate thinking
07:23 -Do all the vector-vector sums
07:39 -When doing math by hand, spend the extra time to track your steps
07:59 -Check dimensions again
08:28 -We construct output by chunking data into vectors
09:00 -My teaching style: Help you develop great problem-solving skills
09:52 -Problem Solving Step 4: Look back on our solution
10:10 -When doing math, it’s good to be able to solve in many different ways
10:21 -Using Octave Online to verify our results
10:35 -Enter matrix A in Octave: comma delimit columns, semicolon delimit rows
11:26 -Enter vector x in Octave
11:37 -Output vector b equals A times x
11:52 -We now have two ways to check our work
12:02 -Octave syntax is compatible with MATLAB
12:29 -Look back by recapitulating the results we achieved.
14:04 -Community Challenge: How can you do this operation differently?
14:23 -Conclusion


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