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Use the fact that matrices A and B are row-equivalent. 121 0 0 251 10 372 2-2 493-2 6 10 30-4 01-10 2 0001-2 00 00 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. A= 41 (c) Find a basis for the row space of A. EEEE 41 (d) Find a basis for the column space of A. 11 (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (f) Let the columns of A be denoted by a, a, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.) (a₁, 82, 84) (a, a, a) (a, a, as)

Use the fact that matrices A and B are row-equivalent. 121 0 0 251 10 372 2-2 493-2 6 10 30-4 01-10 2 0001-2 00 00 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. A= 41 (c) Find a basis for the row space of A. EEEE 41 (d) Find a basis for the column space of A. 11 (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (f) Let the columns of A be denoted by a, a, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.) (a₁, 82, 84) (a, a, a) (a, a, as)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the fact that matrices A and B are row-equivalent. 2 1 0 0 1 0 2-2 A = B = 25 1 372 49 3-2 6, 10 3 0-4 0 1 0 0 L00 00 1 0 2 0 1 -2 (a) Find the rank and nullity of A. rank nullity (b) Find basis for the nullspace of A. ↓ ↑ (c) Find basis for the row space of A. 000 000 (d) Find basis for the column space of A. (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (f) Let the columns of A be denoted by a₁, 32, 33, 34, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) {a₁, 32, 34} O {a₁, az, a3} O {a₁, a3, a5}
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. 2 1 0 0 1 0 2-2 A = B = 25 1 372 49 3-2 6, 10 3 0-4 0 1 0 0 L00 00 1 0 2 0 1 -2 (a) Find the rank and nullity of A. rank nullity (b) Find basis for the nullspace of A. ↓ ↑ (c) Find basis for the row space of A. 000 000 (d) Find basis for the column space of A. (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (f) Let the columns of A be denoted by a₁, 32, 33, 34, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) {a₁, 32, 34} O {a₁, az, a3} O {a₁, a3, a5}
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