Linear Algebra 8j: The Simplest Possible System

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[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@antonellomascarello4698]

I really love these "simple" exercises...I'm enjoying this linear algebra series a lot !!! Thank you Professor 🙂🙏 Greetings from Italy 🇮🇹

[@jackozeehakkjuz]

This video is truly enlightening. Thank you very much!

[@ashishchambyal8019]

Thank you :-)

[@noamza]

This video is confusing for the third example where 0x = 10, while no solution exists, doesn't the null space still contain the [1] vector? A better explanation of this would be appreciated

[@vikasreddykatta5188]

Yes, in the example 0x=10, null space is N = alpha * [1], while the column space is R = {[0]}. For any linear system, the RHS should fall in the column space. In other words, RHS should be a linear decomposition of the columns, for the solution to exist. There is no possible way to decompose [10] vector in terms of [0] vector. Also, we worry about Null space only when there is at least one solution, to see if more solutions are possible, because of dependence among columns.