Question

Help please I need this done like right now

Answer 1

`\left(\begin{array}{c}-24\\20\end{array}\right)`

Explanation:

Given vectors:

`\textbf{a}=\left(\begin{array}{c}-9\\7\end{array}\right)\\\\\\ \textbf{b}=\left(\begin{array}{c}12\\-20\end{array}\right)\\\\\\\textbf{c}=\left(\begin{array}{c}0\\-16\end{array}\right)`

`\textsf{To calculate}\;\;3\textbf{a}-(1)/(4)(\textbf{c}-\textbf{b}),\;\;\textsf{substitute the given vectors into the expression:}`

`3\left(\begin{array}{c}-9\\7\end{array}\right)-(1)/(4)\left(\begin{array}{ccc}0&-&12\\-16&-&(-20)\end{array}\right)`

When subtracting vectors, we subtract the elements in the same position from one vector from the elements in the same position of the other vector. Therefore, subtracting vector b from vector c gives:

`3\left(\begin{array}{c}-9\\7\end{array}\right)-(1)/(4)\left(\begin{array}{c}-12\\4\end{array}\right)`

When multiplying a vector by a constant, we multiply each component of the vector by that constant. Therefore, multiplying vector a by 3 gives:

`\left(\begin{array}{c}3\cdot(-9)\\3\cdot 7\end{array}\right)-(1)/(4)\left(\begin{array}{c}-12\\4\end{array}\right)`

`\left(\begin{array}{c}-27\\21\end{array}\right)-(1)/(4)\left(\begin{array}{c}-12\\4\end{array}\right)`

Multiply (c - b) by 1/4:

`\left(\begin{array}{c}-27\\21\end{array}\right)-\left(\begin{array}{c}-12\cdot (1)/(4)\\4\cdot (1)/(4)\end{array}\right)`

`\left(\begin{array}{c}-27\\21\end{array}\right)-\left(\begin{array}{c}-3\\1\end{array}\right)`

Finally, subtract the vectors:

`\left(\begin{array}{ccc}-27&-&(-3)\\21&-&1\end{array}\right)`

`\left(\begin{array}{c}-24\\20\end{array}\right)`

`\textsf{So,}\;\;3\textbf{a}-(1)/(4)(\textbf{c}-\textbf{b})\;\;\textsf{is equal to}\;\;\left(\begin{array}{c}-24\\20\end{array}\right).`