Question

if alpha=(x1;y1) and beta=(x2;y2)
then (x1;y1)+(x2;y2)=(x1+x2+1;y1+y2-2)
and
a*(x1;y1)=(ax1+a-1;y1+y2-2).
prove that a(alpha+beta)=a(alpha)+a(beta)

Answer 1

this are vector

Answer 2

according to the rule given:\[a\langle x_1,y_1\rangle=\langle ax_1+a-1,y_1+y_2-2\rangle\]is that right?

Answer 3

seems like there might be a typo...please double-check

Answer 4

no is like this .

Answer 5

so we know that\[\alpha+\beta=\langle x_1,y_1\rangle=\langle x_2,y_2\rangle=\langle x_1+x_2+1,y_1+y_2-2\rangle=\langle z_1,z_2\rangle\]and\[a\alpha=a\langle x_1,y_1\rangle=\langle ax_1+a-1,y_1+y_2-2\rangle\]\[a\beta=a\langle x_2,y_2\rangle=\langle ax_2+a-1,y_1+y_2-2\rangle\]hm... this is strange how beta has y1 in it, which makes it depend on alpha
are you *sure* there are no typos?

Answer 6

it is just like this no typus