1 2 1 2 5 1 3 7 2 4 9 3 -1 A = 2 -2 4 1 0 0 1 -1 0 0 0 0 1 -2 3 0 -4 2 B = 0 0 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Use the fact that matrices A and B are row-equivalent.
[1 2 1
2 5 1
1
A =
3 7 2
2 -2
4 9 3 -1
4
1 0
3 0 -4
0 1 -1 0
0 0 0 1 -2
0 0 0 0
2
B =
(a) Find the rank and nullity of A.
rank
nullity
(b) Find a basis for the nullspace of A.
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. [1 2 1 2 5 1 1 A = 3 7 2 2 -2 4 9 3 -1 4 1 0 3 0 -4 0 1 -1 0 0 0 0 1 -2 0 0 0 0 2 B = (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 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 a,, az, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.)
O {a,, a2, a4}
O {a1, az, a3}
O {a1, a3, a5}
Transcribed Image Text:(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. O independent O dependent (f) Let the columns of A be denoted by a,, az, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.) O {a,, a2, a4} O {a1, az, a3} O {a1, a3, a5}
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