Find the dimension of the space P5 Please explain Find the d

Find the dimension of the space P_{5? Please explain}

Find the dimension of the space P5 (enter the integer only without a decimal point or spaces).

Solution

P5 will have a dimension of 6.

P5 is basically a 5th order polynomial, so it must contain [1,x,x²,x³,x⁴,x⁵]. SInce there are 6 elements in the set, thus the dimension of P5 will be 6.