Question-1

If \(x=(1,2)\) and \(y=(2,3)\) are two vectors, compute the following vectors

• \(x+y\)

• \(x-y\)

• \(2x\)

• \(3y\)

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Addition of vectors happens component wise. We have:

\[ \begin{aligned} x+y & =(1,2)+(2,3)=(3,5)\\ x-y & =(1,2)-(2,3)=(-1,-1) \end{aligned} \]

Multiplying a vector by a scalar is done by multiplying each component of the vector by the scalar.

\[ \begin{aligned} 2x & =2(1,2)=(2,4)\\ 3y & =3(2,3)=(6,9) \end{aligned} \]