Which of the following statements are true or false and saywhy: a) If f and g ar

Question

Which of the following statements are true or false and saywhy: a) If f and g are polynomials of degreen, then f+g is apolynomial of degree n. b) A nonzero scalar of F may be considered to be a polynomialin P(F) having degree zero. c) In any vector space ax=ay implies that x=y. d) A vector space in Fn maybe regarded as a matrixin Mn x 1(F). Which of the following statements are true or false and saywhy: a) If f and g are polynomials of degreen, then f+g is apolynomial of degree n. b) A nonzero scalar of F may be considered to be a polynomialin P(F) having degree zero. c) In any vector space ax=ay implies that x=y. d) A vector space in Fn maybe regarded as a matrixin Mn x 1(F).

Explanation / Answer

a is true because you just add the coefficients to the variouspowers of x. b true because cx^0 = c for any nonzero scalar c c no, consider the case where a=0, this tells us nothing about arelation between x and y d it is true if you meant to say vector rather than vectorspace.

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