Question #8026

Geometrically representation of basis of v=(3,4) when v1(1,0) v2(0,1) v=av1+bv2

Expert's answer

v=av1+bv2

Let's denote v={xv,yv}

Then

xv=a*xv1+b*xv2

yv=a*yv1+b*yv2

Substitute corrdinates of v1,v2:

xv=a*1+b*0=3

yv=a*0+b*1=4

These two equations allow us to find a and b:

a*1+b*0=3 => a=3

a*0+b*1=4 => b=4

So we obtain that v=3*v1+4*v2

Let's denote v={xv,yv}

Then

xv=a*xv1+b*xv2

yv=a*yv1+b*yv2

Substitute corrdinates of v1,v2:

xv=a*1+b*0=3

yv=a*0+b*1=4

These two equations allow us to find a and b:

a*1+b*0=3 => a=3

a*0+b*1=4 => b=4

So we obtain that v=3*v1+4*v2

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