9. The nullity of a 3 × 5 matrix(a) is three(b) can be any number from zero to two(c) can be any number from zero to three(d) can be any number from two to five

[Linear Algebra] 5. (a) Construct a matrix B whose null space consists of all linear combinations of vectors (2, 0, 7, 1) and (3, 1, −4, 0). (b) Express matrix B as a sum of two rank one matrices.

Let A be a 3 x 5 matrix. If dim(null(A))=2, then the dimension of the column space of A isSelect one:a. 3b. 1c. 2d. None of the other choices is correct

Use the fact that matrices A and B are row-equivalent.A = −2 −5 8 0 −17 1 3 −5 1 5−5 −9 13 7 −671 7 −13 5 −3B = 1 0 1 0 1 0 1 −2 0 30 0 0 1 −50 0 0 0 0(a) Find the rank and nullity of A.rank nullity     (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. (d) Find a basis for the column space of A. (e) Determine whether or not the rows of A are linearly independent.independentdependent    (f) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.){a1, a2, a4}{a1, a2, a3}{a1, a3, a5}

[a b c] is a:Question 4Answera.Row matrix.b.Diagonal matrix.c.Column matrix.d.Zero matrix.

Consider the matrix . Which of the following statements is correct?Question 1Select one:Select one:a.None of the other statements are correct.b.The matrix is invertible and its determinant is not equal to zero.c.The matrix is not invertible and its determinant is not equal to zero.d.The matrix is not invertible and its determinant is equal to zero.e.The matrix is invertible and its determinant is equal to zero.