Question

Is {sinx, cosx, sin(x+π/4)} a linearly independent set over R ? Justify our answer

Answer 1

Yes the set $( sinx,cosx,sin(x+\dfrac{\pi}{4}))$ is linearly independent over R

Because,

For the linear independency,

$(asinx+bcos+csin(x+\dfrac{\pi}{4})) = 0$ for only $a= b=c=0$

Hence, we get only one value of $a, b$ and $c$ for which it is zero i.e. 0

Therefore, the set is linearly independent.