Review exercise 1.11. Suppose is a 2 by 2 matrix that adds the first equation of a linear system to the second equation. What is ? ? ?
Answer: Since adds the first equation to the second, we have
We then have
In general if for some we have
then for we have
Since for we have
by induction for all we have
Finally, we have
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.