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Mars2501 [29]
4 years ago
7

PLEASE ANSWER QUICKLY ASAP ANSWER QUESTION A AND B​

Mathematics
1 answer:
Evgen [1.6K]4 years ago
4 0

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

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