Wanted to ask a question in reference to lecture 3. Around minute 14 Prof Strang uses the example of a column times a row which yields a 3x2 matrix (3 rows, 2 columns). What would be the answer if using the same example, the row ([1 6]) were on the left? He says row times column is different than column times tow and I'm curious about the outcome.

Question

Wanted to ask a question in reference to lecture 3.  Around minute 14 Prof Strang uses the example of a column times a row which yields a 3x2 matrix (3 rows, 2 columns).  What would be the answer if using the same example, the row ([1 6]) were on the left?  He says row times column is different than column times tow and I'm curious about the outcome.

anonymous · Answer

You can multiply a 3x1 matrix (left side) by a 1x2 matrix (right side) because the number of columns of the left side and the number of rows on the right side are the same, both 1.

You cannot multiply a 1x2 (left side) by a 3x1 (right side) because the number of columns on the left side is 2, which is not equal to the number of rows on the right side, 3.

However, let's change the problem to multiplying a 1x2 (left side) by a 2x1 (right side). Then the result is a 1x1 matrix, or just a number. Essentially, this is a dot product.