32) As a mathematical tool, determinants are of value in helping to solve a series of simultaneous equations.

33) A set of simultaneous equationscan be solved through the use of determinants by setting up a proportion of two special determinants for each unknown variable.

34) To create the transpose of a given matrix, we simply interchange the rows with the columns.

35) A matrix is

A) a determination of probability.

B) a qualitative tool used to solve a set of simultaneous equations.

C) an array of numbers.

D) a single column of non-zero numbers.

E) None of the above

36) The value of the determinant is

A) ab – cd.

B) ac – bd.

C) ab + cd.

D) ac + bd.

E) ad – cb.

37) The correct determinant value for the determinant would be

A) (8)(4)(3)(6).

B) (8)(4) + (3)(6).

C) (8)(4) – (3)(6).

D) (8)(3) – (6)(4).

E) (8)(6) – (3)(4).

38) An n × m matrix, when added to an n × m matrix, yields

A) an n × m matrix.

B) an m × n matrix.

C) a 2(n × m) matrix.

D) a 2n × 2m matrix.

E) None of the above

39) An n × m matrix, when added to an m × n matrix, yields

A) an n × m matrix.

B) an m × n matrix.

C) a 2(n × m) matrix.

D) a 2n × 2m matrix.

E) None of the above

40) An n × m matrix, when multiplied by an n × m matrix, yields

A) an n × m matrix.

B) an m × n matrix.

C) an n2 × m2 matrix.

D) an (n × m)2 matrix.

E) None of the above

41) An n × m matrix, when multiplied by an m × n matrix, yields

A) an n × m matrix.

B) an m × n matrix.

C) an n × n matrix.

D) an n × m × n matrix.

E) None of the above

42) An n × n matrix, when multiplied by an n × n matrix, yields

A) an n × n matrix.

B) a 2n matrix.

C) an n2 + n2 matrix.

D) an (n × n)2 matrix.

E) None of the above

43) An n × m matrix, when multiplied by an m × p matrix, yields

A) an n × m × m × p matrix.

B) an n × m × p matrix.

C) an n × p matrix.

D) a p matrix.

E) None of the above

44) Add the matrices +

A)

B)

C)

D)

E) cannot be added

45) Element 1,1 of the inverse of the matrix is

A) -5.

B) -4.

C) 3.

D) 7.

E) None of the above