The nullspace of a matrix aa is the solution space of the homogeneous system ax=0ax=0. b. a linear system is solvable if and only if the vector of constants belongs to the column space of the coefficient matrix of the system. c. a subspace of a vector space vv cannot contain only a finite number of elements. d. the span of the columns of a matrix is called the column space of the matrix. e. a nonempty subset ww of some vector space vv is called a subspace of vv if ww is closed under linear combinations. f. the set of all vectors of the form [1,x, y]t[1,x, y]t, where xx and yy range over all real numbers, is a subspace of r3r3. g. the set of all vectors of the form [0,x, y]t[0,x, y]t, where xx and yy range over all real numbers, is a subspace of r3r3. h. none of the above

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

hello,

as we don't know if g(x) is continue,

answer b

f(x)=2x²-8x+1=2(x²-4x+4)+1-8=2(x-2)²-7

vertex is (2,-7) ( a minimum since coefficient of x² is > 0)

b and c are the correct answers.

good luck on the quiz! : d