Question

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Part IV – True or False Each question is worth 1 point. For each of the following statements, determine whether it is true or false (circle the answer; you don't need to show any work). 1. True or False: The rank of a square matrix equals its order (size) if and only if its determinant is nonzero. 2. True or False: A homogeneous system of linear equations always has a solution. 3. True or False: If A and B are invertible square matrices of the same size, then AB is also invertible, and (AB)-1 = A-B-1, 4. True or False: Switching two rows in a matrix preserves its rank. 5. True or False: For a function of two variables f(x, y), the gradient vector Vf is tangent to the level curve f(x,y) = 0. 6. True or False: If two lines in the three-dimensional space don't intersect, then they are parallel 7. True or False: The value of the triple scalar product of three vectors depends on the order of the vectors. 8. True or False: For differentiable vector functions f(t) and g(t), the Product Rule for Cross Products states that (f(t) x g(t)) = f'(t) g(t) +g'(t) x f(t). 9. True or False: n! gives the number of permutations of n distinguishable objects. 10. True or False: If two events cannot happen simultaneously, they are independent. 11. True or False: For a binomial distribution, u = np. 12. True or False: Sampling without replacement obeys the hypergeometric distribution law.

Answer 1

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