In Exercises 66 and 67, use the fact that matrices A and B are row-equivalent. (a) Find the rank and nullity of A. (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. (f) Let the columns of A be denoted by a₁, a2, a3, a4, and as. Which of the following sets is (are) linearly independent? (ii) {a₁, a₂, a3} (iii) {a₁, a3, as} (i) {a₁, a₂, a4} 66. A = B 1 25 234 1 0 0 1 1 0 7 4 9 1 0 23 2 2 -2 -1 4 0 1 - -1 31 3 0 - 0 = 0 0 0 1 -2 422 4 2 0 00 0 0

In Exercises 66 and 67, use the fact that matrices A and B are row-equivalent. (a) Find the rank and nullity of A. (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. (f) Let the columns of A be denoted by a₁, a2, a3, a4, and as. Which of the following sets is (are) linearly independent? (ii) {a₁, a₂, a3} (iii) {a₁, a3, as} (i) {a₁, a₂, a4} 66. A = B 1 25 234 1 0 0 1 1 0 7 4 9 1 0 23 2 2 -2 -1 4 0 1 - -1 31 3 0 - 0 = 0 0 0 1 -2 422 4 2 0 00 0 0

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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