For each of the following matrices A: (i) find its rref R; (ii) find the rref R' of AT; (iii) find a basis for rowspace(A), colspace(A), and nullspace(A), if possible, using only the information found in A and R. (iv) Find a basis for nullspace(A") using only the information found in R'. Practice sight-reading the nullspaces. (v) State the rank and nullity of A and AT, and verify that the Dimension Theorem is satisfied by both A and AT. (vi) Decide if A is full-rank or not. Use technology if allowed by your instructor. 3 -4 1 -2 2 -6 5 -5 -2 3 -2 7 a. A = -3 9 -6 b. A = -4 -3 -9 -2 6 1 -13 7 -5 6. 6.
For each of the following matrices A: (i) find its rref R; (ii) find the rref R' of AT; (iii) find a basis for rowspace(A), colspace(A), and nullspace(A), if possible, using only the information found in A and R. (iv) Find a basis for nullspace(A") using only the information found in R'. Practice sight-reading the nullspaces. (v) State the rank and nullity of A and AT, and verify that the Dimension Theorem is satisfied by both A and AT. (vi) Decide if A is full-rank or not. Use technology if allowed by your instructor. 3 -4 1 -2 2 -6 5 -5 -2 3 -2 7 a. A = -3 9 -6 b. A = -4 -3 -9 -2 6 1 -13 7 -5 6. 6.
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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2.3 #2
Transcribed Image Text:For each of the following matrices A: (i) find its rref R; (ii) find the rref R' of AT; (iii)
find a basis for rowspace(A), colspace(A), and nullspace(A), if possible, using only the
information found in A and R. (iv) Find a basis for nullspace(AT) using only the
information found in R'. Practice sight-reading the nullspaces. (v) State the rank and
nullity of A and AT, and verify that the Dimension Theorem is satisfied by both A and
AT. (vi) Decide if A is full-rank or not. Use technology if allowed by your instructor.
2.
3 -4
1
-2
2 -6 5
-5
-2 3
-2 7
a. A =
-3 9 -6
3
b. A =
%3D
-4 2 -3 -9
-2 6 1 -13
7 -5 6 6
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