For each matrix A, determine if col A = R^3. 15. [1 2 3 0 4 5 0 0 6] 16. [1 -1 1

Question

For each matrix A, determine if col A = R^3. 15. [1 2 3 0 4 5 0 0 6] 16. [1 -1 1 -1 1 -1 1 -1 1] Give a condition that will imply that an n times n upper (lower) triangular matrix A has col A = R^n. Suppose you are given a 10 times 12 homogeneous linear system Ax = 0. You find that all solutions can be generated from just two solutions, neither a scalar multiple of the other. Discuss whether or not the corresponding non-homogeneous system Ax = b has a solution for every vector b. 19. If A is a 6 times 7 matrix, what is the largest possible dimension of col A? If A is a 7 times 6 matrix and dim null A = 2, What is the dimension of row A? If A is a 6 times 8 matrix, what is the smallest possible dimension of null A?

Explanation / Answer

21).

By the rank-nullity theorem for an m x n matrix

Rank A+Nullity A=n

Since the Rank of a 6x8 can be up to and including 8 , the Nullity can be 0.

null A =0

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.