Let p, (1) = 2 +?, P2(t) =t-4², p3(t) = 3 +t- 3r?. Complete parts (a) and (b) below. a. Use coordinate vectors to show that these polynomials form a basis for P2. What are the coordinate vectors corresponding to p1, P2, and p3? P1 = . P2 = P3 Place these coordinate vectors into the columns of a matrix A. What can be said about the matrix A? O A. The matrix A is invertible because it is row equivalent to lą and therefore the null space of A, denoted Nul A, forms a basis for R3 by the Invertible Matrix Theorem. O B. The matrix A is invertible because it is row equivalent to lą and therefore the row reduced columns of A form a basis for R3 by the Invertible Matrix Theorem. O C. The matrix A is invertible because it is row equivalent to lz and therefore the original columns of A form a basis for R° by the Invertible Matrix Theorem. D. The matrix A forms a basis for R° by the Invertible Matrix Theorem because all square matrices are row equivalent to l3. How does this show that the polynomials form a basis for P2? O A. The polynomials form a basis for P, because of the isomorphism between R and P,. B. The polynomials form a basis for P2 because the matrix A is invertible. OC. The polynomials form a basis for P2 because the columns of A are linearly independent. D. The polynomials form a basis for P, because any basis in R" is also a basis in P,. -2 b. Consider the basis B= {p1, P2, P3} for P2. Find q in P2, given that [q]g = 1 2 q(1) = (O + Ot+ O?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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The polynomials and belongs to the vector space because
contains all the polynomials of degree less than or equal to 2 with their
coefficients in .
We have to create a matrix A with the help of the coordinate vectors of the
given polynomials.
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