## Linear Algebra and Its Applications, Exercise 2.6.2

Exercise 2.6.2. Specify the 2 by 2 matrix that has the following effects:

1. projecting all vectors onto the $x$ axis
2. projecting the resulting vectors onto the $y$ axis

Answer: From the discussion in the first part of section 2.6 we know that the matrix $\begin{bmatrix} 1&0 \\ 0&0 \end{bmatrix}$

will project vectors onto the $x$ axis.

Similarly the matrix $\begin{bmatrix} 0&0 \\ 0&1 \end{bmatrix}$

will project vectors onto the $y$ axis.

To accomplish both operations in succession we therefore need to multiply vectors by the first matrix and then by the second; this corresponds to multiplying vectors by the product matrix $\begin{bmatrix} 0&0 \\ 0&1 \end{bmatrix} \begin{bmatrix} 1&0 \\ 0&0 \end{bmatrix} = \begin{bmatrix} 0&0 \\ 0&0 \end{bmatrix}$

Note that the resulting matrix projects all vectors onto the origin.

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 .

This entry was posted in linear algebra. Bookmark the permalink.