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You can think about a space of polynomials of maximum degree 3. This is a linear space on real numbers. (Prove it). Then what is it's basic? Obviously {1$1$,t$t$,t^2$t^2$} gives you three linear independent vectors and they span all vector space. So, what we have is actually that you can see that this problem is not different from saying that 1=e_1$1=e_1$, t=e_2$t=e_2$, t^2=e_3$t^2=e_3$ where we just renamed those vectors.
Briefly,
You can think about a space of polynomials of maximum degree 3. This is a linear space on real numbers. (Prove it). Then what is it's basic? Obviously {1,t,t^2} gives you three linear independent vectors and they span all vector space. So, what we have is actually that you can see that this problem is not different from saying that 1=e_1, t=e_2, t^2=e_3 where we just renamed those vectors.
Briefly,
You can think about a space of polynomials of maximum degree 3. This is a linear space on real numbers. (Prove it). Then what is it's basic? Obviously {$1$,$t$,$t^2$} gives you three linear independent vectors and they span all vector space. So, what we have is actually that you can see that this problem is not different from saying that $1=e_1$, $t=e_2$, $t^2=e_3$ where we just renamed those vectors.
Briefly,
You can think about a space of polynomials of maximum degree 3. This is a linear space on real numbers. (Prove it). Then what is it's basic? Obviously {1,t,t^2} gives you three linear independent vectors and they span all vector space. So, what we have is actually that you can see that this problem is not different from saying that 1=e_1, t=e_2, t^2=e_3 where we just renamed those vectors.
