his test: 30 point(s) possible This question: 5 point(s) possible Submit test If B is the standard basis of the space P of polynomials, then let B = {1,t,t2,to]. Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. 1+ 912 - +3, 1+ 6+ 3 , 1 + + + 91 2 Write the coordinate vector for the polynomial 1+ 912 - 3 Write the coordinate vector for the polynomial t + 6t3 Write the coordinate vector for the polynomial 1 + t+ 912. To test the linear independence of the set of polynomials, row reduce the matrix which is formed by making each coordinate vector a column of the matrix. If possible, write the matrix in reduced echelon form. 101 0 1 1 909 -160 Are the polynomials linearly independent? O A. Since the matrix has a pivot in each column, its columns (and thus the given polynomials) are not linearly independent. O B. Since the matrix does not have a pivot in each column, its columns (and thus the given polynomials) are not linearly independent. O C. Since the matrix has a pivot in each column, its columns (and thus the given polynomials) are linearly independent. O D. Since the matrix does not have a pivot in each column, its columns (and thus the given polynomials) are linearly independent