Use the fact that matrices A and B are row-equivalent. 1 2 10 0 11 0 A = B = 25 3 7 22-2 14 32 10 2 4 10 30-4 01-10 2 0 1 -2 00 ,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. E (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

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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Use the fact that matrices A and B are row-equivalent.
1 2 10
2 5 11
37 22-2
14 32 10 2 4
10 30-4
01-10 2
0001-2
0 0 0 0 0
(a) Find the rank and nullity of A.
rank
nullity
A =
B =
NOO
(b) Find a basis for the nullspace of A.
(c) Find a basis for the row space of A.
18=888;
E
(d) Find a basis for the column space of A.
O dependent
1
(e) Determine whether or not the rows of A are linearly independent.
independent
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. 1 2 10 2 5 11 37 22-2 14 32 10 2 4 10 30-4 01-10 2 0001-2 0 0 0 0 0 (a) Find the rank and nullity of A. rank nullity A = B = NOO (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. 18=888; E (d) Find a basis for the column space of A. O dependent 1 (e) Determine whether or not the rows of A are linearly independent. independent
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(f) Let the columns of A be denoted by a₁, ₂, 3, 4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.)
Ⓒ (a₁, az, a4)
(a₁, az, a3)
{a₁, a3, a5)
Transcribed Image Text:(f) Let the columns of A be denoted by a₁, ₂, 3, 4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.) Ⓒ (a₁, az, a4) (a₁, az, a3) {a₁, a3, a5)
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