Review exercise 1.13. Given the following:

use the triangular systems and to find a solution to

Answer: We have

Since and we have also. Since we have so that

We then have

Since and we have . We then have so that and

Note that is equal to the last column of the 3 by 3 identity matrix . Since is nonsingular we know that exists, and since we have we see that the solution is equal to the last column of .

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.