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(a)
(b)
Are there values of r and s for which
13.
has rank 1 or 2? If so, find those values. in for which the matrix
Use the result in Exercise 10 to show that the set of points
14.
has rank 1 is the curve with parametric equations , ,.
Prove: If , then A and have the same rank.
15.
16. matrix whose column space is a plane through the origin in
(a) Give an example of a
3-space.
(b) What kind of geometric object is the nullspace of your matrix?
(c) What kind of geometric object is the row space of your matrix?
(d) In general, if the column space of a matrix is a plane through the origin in 3-space,
what can you say about the geometric properties of the nullspace and row space? Explain
your reasoning.
Indicate whether each statement is always true or sometimes false. Justify your answer by giving
17. a logical argument or a counterexample.
(a) If A is not square, then the row vectors of A must be linearly dependent.
