1 Answer

Acoiro · Answer 1 · 2021-10-23T23:25:05+0000

Answer:

a)
$a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}$

b) (i)
$a+2c=\begin{pmatrix}-4\\2\end{pmatrix}$

(ii)
k=2

Explanation:

It is given that,

$a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}$

a)

We need to find the value of a+b+c.

$a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}$

$a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}$

$a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}$

b)

(i) We need to find the value of a+2c.

$a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}$

$a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}$

$a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}$

$a+2c=\begin{pmatrix}-4\\2\end{pmatrix}$

(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.

$a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}$

$\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}$

On comparing both sides, we get

k=2

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