Chap 28 Exercises

\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]

Exercise 1 Note: The radio-button multiple choice questions don’t allow us to display a column vector as such. Instead, we use the notation involving a superscript T. For instance, \((2, -3)^T\) is a column vector which we would ordinarily write \(\left(\begin{array}{c}2\\-3\end{array}\right)\) A vector written like \((2, -3)\), without the \(^T\), is a row vector.

Suppose \[\vec{\mathbf{u}} \equiv \left(\begin{array}{c}2\\-3\end{array}\right) \ \ \hbox{and}\ \ \vec{\mathbf{v}} \equiv \left(\begin{array}{c}4\\1\end{array}\right)\] Compute the following linear combinations (arithmetically) …

  1. \(- \vec{\mathbf{u}} -8 \vec{\mathbf{v}}\)

\((-34, -5)^T\)

\((-34, -5)\)

\((-34, 15)\)

\((34, 15)^T\)

Invalid combination

question id: beech-iron-clock-1

  1. \(2.1 \vec{\mathbf{u}} -1.3 \vec{\mathbf{v}}\)

\((-1, -7.6)^T\)

\((0.8)\)

\((-1, -7.6)\)

\((2.1, -1.3)^T\)

Invalid combination

question id: beech-iron-clock-2

  1. \(-0.5 \vec{\mathbf{u}} + 3.2 \vec{\mathbf{v}}\)

\((11.8, 4.7)^T\)

\((2.7)\)

\((13.8, 1.7)\)

\((34, 16)^T\)

Invalid combination

question id: beech-iron-clock-3

  1. \(7 \vec{\mathbf{u}} + 5 \vec{\mathbf{v}}\)

\((34, -16)^T\)

\((32, -14)^T\)

\((34, -14)^T\)

\((32, -16)^T\)

Invalid combination

question id: beech-iron-clock-4

Exercise 2 Here are some vectors to use in answering the following questions.

\[\vec{u} \equiv \left[\begin{array}{r} -100\\\ 98\\\ 9\\ -81\\\ 90\end{array}\right]\ \ \ \vec{v} \equiv \left[\begin{array}{r}\ 21\\\ 37\\\ 93\\ -41\\ -93\end{array}\right]\ \ \ \vec{w} \equiv \left[\begin{array}{r} -97\\ -11\\\ 33\\ -49\\\ 91\end{array}\right]\]

Calculate the length of each of these vectors in the corresponding interactive R chunk.

  1.         \(2 \vec{u}\)
  1.       \(- 2 \vec{u}\)
  1.         \(4 \vec{u}\)
  1.         \(17 \vec{v}\)
  1.      \(- 1.5 \vec{w}\)

Exercise 3 Using R/mosaic and the %dot% and sqrt() functions, calculate the length of each of these vectors:

  1. \(\vec{u} \equiv \left[\begin{array}{r}\ 35\\ -93\\ -99\end{array}\right]\)
  1. \(\vec{v} \equiv \left[\begin{array}{r} -59\\\ 41\\ -41\end{array}\right]\)
  1. \(\vec{w} \equiv \left[\begin{array}{r} -76\\ -71\\ -48\end{array}\right]\)
  1. \(\vec{x} \equiv \left[\begin{array}{r} -96\\\ 83\\\ 35\end{array}\right]\)

Exercise 4  

{{< include ./Block_3/girl-send-scarf.qmd >}}

Exercise 5  

{{< include ./Block_3/tiger-run-futon.qmd >}}

Exercise 6  

{{< include ./Block_3/kangaroo-have-closet.qmd >}}

Exercise 7  

{{< include ./Block_3/lamb-throw-candy.qmd >}}

Exercise 8  

{{< include ./Block_3/panda-think-plate.qmd >}}

Exercise 9  

{{< include ./Block_3/duck-do-pantry.qmd >}}

Exercise 10  

{{< include ./Block_3/crocodile-talk-mattress.qmd >}}

Activities

Exercise 11  

{{< include ./Block_3/duck-do-pantry.qmd >}}

Exercise 12  

{{< include ./Block_3/snake-choose-ring.qmd >}}
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