## Linear Algebra and Its Applications, Exercise 3.3.25

Exercise 3.3.25. Given the measurements $y = 2, 0, -3, -5$ at $t= -1, 0, 1, 2$ from the previous exercise, what would be the coefficient matrix $A$, the unknown vector $x$, and the data vector $b$ if we wish to fit the data using a parabola of the form $y = C + Dt + Et^2$?

Answer: We would need to change the unknown vector $x$ to add the additional unknown parameter $E$ and add a third column to the coefficient matrix $A$ to reflect the values of $t^2$ for the various measurements. The vector $b$ containing the data values would remain the same. The system $Ax = b$ would then be as follows: $\begin{bmatrix} 1&-1&1 \\ 1&0&0 \\ 1&1&1 \\ 1&2&4 \end{bmatrix} \begin{bmatrix} C \\ D \\ E \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \\ -3 \\ -5 \end{bmatrix}$

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 .

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