Exercise 3.4.2. Given two orthonormal vectors and
and the vector
, project
onto
and
. Also find the projection
of
onto the plane formed by
and
.
Answer: Since is orthonormal, the projection of
onto
is given by
Similarly the projection of onto
is given by
The projection of
onto the plane formed by
and
is simply the sum of the projections above:
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, Fifth Edition
and the accompanying free online course, and Dr Strang’s other books
.