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#ret #hw
1 Solving Systems
Read 1.B! Have questions. Try a couple exercises. notes: KBxChapter1B
Also, keep thinking about the group work questions from today:
- What is the relationship between cross product and the magnitude of a
vector?
- Which vector? Assuming resultant vector, \(||a||b|sin(\theta)|\) would be the magnitude
- How does cosine relate to dot product? Can you prove it? (HINT: think
about the previous problem and the Law of Cosines.)
- \(a \cdot b = |a||b|cos(\theta)\)
- [abcosthetaproof.pdf]
- *Do your best to solve the following matrix equation using matrix multiplications that correspond to row operations for systems, specifically multiplying a row by a scalar, adding two rows, and swapping the order of rows. You'll have to think about how to do these things with matrices! It may help to keep in mind what a SOLVED matrix equation looks like (in particular, what does the 3x3 matrix of coefficients look like?).*
\[
\begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & 1\\ 2 & 1 & -2 \\ \end{bmatrix}⋅
\begin{bmatrix} x \\ y \\ z \\ \end{bmatrix}=
\begin{bmatrix} -2 \\ 3 \\ 2 \\ \end{bmatrix}\]
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