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Use the fact that matrices A and B are row-equivalent. 1 2 1 0 0 2 5 1 1 0 A = 3 7 2 2-2 9 20 7 -2 8 1 0 30-4 0 1 -1 0 2 8 = 0 1 -2 00 00 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. WNH ↓ 1 BEEBE: DI ↓1 (d) Find a basis for the column space of A. ↓1 (e) Determine whether or not the rows of A are linearly independent. O independent dependent (f) Let the columns of A be denoted by a₁, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a1, az, a4) {a₁, az, aç} O {a1, a3, a5)

Use the fact that matrices A and B are row-equivalent. 1 2 1 0 0 2 5 1 1 0 A = 3 7 2 2-2 9 20 7 -2 8 1 0 30-4 0 1 -1 0 2 8 = 0 1 -2 00 00 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. WNH ↓ 1 BEEBE: DI ↓1 (d) Find a basis for the column space of A. ↓1 (e) Determine whether or not the rows of A are linearly independent. O independent dependent (f) Let the columns of A be denoted by a₁, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a1, az, a4) {a₁, az, aç} O {a1, a3, a5)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 23EQ
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Use the fact that matrices A and B are row-equivalent. 1 2 1 0 0 2 5 1 1 0 A = 3 7 2 2 -2 9 20 7 -2 8 1 0 30-4 0 1 -1 0 2 8 = 0 0 0 1 -2 0 0 00 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. ↓↑ (c) Find a basis for the row space of A. (68883-1 (d) Find a basis for the column space of A. ↓t (e) Determine whether or not the rows of A are linearly independent. O independent dependent (f) Let the columns of A be denoted by a₁, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a1, az, a4}) O {a1, a2, a3} O {a1, a3, a5}
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. 1 2 1 0 0 2 5 1 1 0 A = 3 7 2 2 -2 9 20 7 -2 8 1 0 30-4 0 1 -1 0 2 8 = 0 0 0 1 -2 0 0 00 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. ↓↑ (c) Find a basis for the row space of A. (68883-1 (d) Find a basis for the column space of A. ↓t (e) Determine whether or not the rows of A are linearly independent. O independent dependent (f) Let the columns of A be denoted by a₁, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a1, az, a4}) O {a1, a2, a3} O {a1, a3, a5}
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