Label the following statements as 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) A vector in Fn may be regarded as a matrix in Mn×1(F ). (f)An m × 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 scalar of F may be considered to be a polynomial in P(F) having degree zero. (k) Two functions in F(S, F) are equal if and only if they have the same value at each element of S.
Label the following statements as 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) A vector in Fn may be regarded as a matrix in Mn×1(F ).
(f)An m × 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 scalar of F may be considered to be a polynomial in P(F) having degree zero.
(k) Two functions in F(S, F) are equal if and only if they have the same value at each element of S.
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