a) a as a column vector is [tex]\left(\begin{array}{c}1\\-2\end{array}\right)[/tex]
b) 2a -b as a column vector is [tex]\left(\begin{array}{c}1\\-7\end{array}\right)[/tex]
Vectors
To write a vector as a column vector, the number at the top is the magnitude of the x component (horizontal component) of the vector and the number at the bottom is the magnitude of the y component (vertical component) of the vector
Magnitude of the vertical component = 1
Magnitude of the vertical component = -2
NOTE: Negative sign indicates that the direction of the vector is downwards
Thus, vector a as a column vector is
[tex]a = \left(\begin{array}{c}1\\-2\end{array}\right)[/tex]
Hence, a as a column vector is [tex]\left(\begin{array}{c}1\\-2\end{array}\right)[/tex]
Magnitude of the vertical component = 1
Magnitude of the vertical component = 3
[tex]b = \left(\begin{array}{c}1\\3\end{array}\right)[/tex]
Now, we are to work out 2a - b
That is,
[tex]2a -b = 2 \left(\begin{array}{c}1\\-2\end{array}\right)-\left(\begin{array}{c}1\\3\end{array}\right)[/tex]
[tex]2a -b = \left(\begin{array}{c}2\\-4\end{array}\right)-\left(\begin{array}{c}1\\3\end{array}\right)[/tex]
[tex]2a -b = \left(\begin{array}{c}2-1\\-4-3\end{array}\right)[/tex]
[tex]2a -b = \left(\begin{array}{c}1\\-7\end{array}\right)[/tex]
Hence, 2a -b as a column vector is [tex]\left(\begin{array}{c}1\\-7\end{array}\right)[/tex]
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