Question

PLEASE ANSWER QUICKLY ASAP
ANSWER QUESTION A AND B​

Answer 1

Answer:

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

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

   (ii) $k=2$

Step-by-step 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

$k=2$