1. Label the following statements as being true or false. (a) Every vector space contains a zero vector. (b) A vector space may have more than one zero vector. (c) In any vector space ax = bx implies that a = b. (d) In any vector space ax = ay implies that x = y. (e) An element of F^ may be regarded as an element of Mx1(F). (f) An m x n matrix has m columns and n rows. (g) In P(F) only polynomials of the same degree may be added. (h) If f and g are polynomials of degree n, then f + g is a polynomial of degree n. ) If f is a polynomial of degree n and c is a nonzero scalar, then of is a polynomial of degree n. (1) A nonzero element of F may be considered to be an element of P(F) having degree zero. (k) Two functions in F(S, F) are equal if and only if they have the same values at each element of S.
Label the following statements as being true or false.
(a) Every
(b) A vector space may have more than one zero vector.
(c) In any vector space ax = bx implies that a = b.
(d) In any vector space ax = ay implies that x = y.
(e) An element of F^n may be regarded as an element of Mnx1(F).
(f) An m x n matrix has m columns and n rows.
(g) In P(F) only polynomials of the same degree may be added.
(h) If f and g are polynomials of degree n, then f + g is a polynomial of degree n.
(i) If f is a polynomial of degree n and c is a nonzero scalar, then cf is a polynomial of degree n.
(j) A nonzero element of F may be considered to be an element of P(F) having degree zero.
(k) Two functions in F(S,F) are equal if and only if they have the same values at each element of S.
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