28d4de…: “Rather than a winter castle”

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Compute $\bu +\bv$ where $\bu = \begin {bmatrix} -1\\3\\-7 \end {bmatrix}$ and $\bv = \begin {bmatrix} 2\\0\\4 \end {bmatrix}$

$\bu +\bv = \left [\begin {array}{c} \answer {1}\\\answer {3}\\\answer {-3} \end {array}\right ]$

Compute $3\bu -\bv$ where $\bu = \begin {bmatrix} 0\\1\\-2 \end {bmatrix}$ and $\bv = \begin {bmatrix} -2\\6\\5 \end {bmatrix}$

$3\bu -\bv = \left [\begin {array}{c} \answer {2}\\\answer {-3}\\\answer {-11} \end {array}\right ]$

Write a vector equation equivalent to the system: $\left \{ \begin {array}{rrrrrl} &&x_2&+&x_3 &=-5 \\ -x_1& -&4x_2 &&&=0\\ x_1&+&9x_2&+&6x_3 &= 4\\ \end {array} \right .$

$x_1\left [\begin {array}{c} \answer {0}\\\answer {-1}\\\answer {1} \end {array}\right ] +x_2 \left [\begin {array}{c} \answer {1}\\\answer {-4}\\\answer {9} \end {array}\right ]+x_3\left [\begin {array}{c} \answer {1}\\\answer {0}\\\answer {6} \end {array}\right ] =\left [\begin {array}{c} \answer {-5}\\\answer {0}\\\answer {4} \end {array}\right ]$

Is $\begin {bmatrix} -1\\5\end {bmatrix}$ in Span $\left \{ \begin {bmatrix} 1\\0\end {bmatrix}, \begin {bmatrix} 0\\1\end {bmatrix} \right \}$ ?

Yes No

Let $\bv _1 = \begin {bmatrix} 3\\6\\ 9\end {bmatrix}$ and $\bv _2 = \begin {bmatrix} 2\\4\\6\end {bmatrix}$ . Is Span $\{\bv _1, \bv _2\}$ a line or a plane?

line plane