(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,, a,, ag and a. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a,, a2, ag O {a,, a2, a3} O {a,, a3, as}

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.2: Properties Of Matrrix Operations
Problem 79E
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(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,, az, ag, and ag. Which of the following sets is (are) linearly independent? (Select all that apply.)
O {a,, a2, a4}
O {a,, a2, a3}
O {a,, a3, ag}
Transcribed Image Text:(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,, az, ag, and ag. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a,, a2, a4} O {a,, a2, a3} O {a,, a3, ag}
Use the fact that matrices A and B are row-equivalent.
-2
-5
8 0-17
-5 1
A =
-5 -11
17 3 -53
7 -13 5
1
-3
1 0
10
1
01-20
3
B =
0 0
01-5
0 0 0 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.
(d) Find a basis for
column space of A.
(e) Determine whether or not the rows of A are linearly independent.
O independent
O dependent
00
1 1
00
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. -2 -5 8 0-17 -5 1 A = -5 -11 17 3 -53 7 -13 5 1 -3 1 0 10 1 01-20 3 B = 0 0 01-5 0 0 0 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. (d) Find a basis for column space of A. (e) Determine whether or not the rows of A are linearly independent. O independent O dependent 00 1 1 00
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