Suppose that A = [c, c2 C3] is a 3 × 3 matrix with columns c;, and suppose that a basis for the kernel of A is given by the vector (a) Write and circle an equation involving the c; that shows that the c; are not linearly independent. (b) Since the kernel of A has dimension 1, the image of A has dimension 2, and therefore has a basis consisting of 2 of the c;. Which two make a basis of the image of A?
Suppose that A = [c, c2 C3] is a 3 × 3 matrix with columns c;, and suppose that a basis for the kernel of A is given by the vector (a) Write and circle an equation involving the c; that shows that the c; are not linearly independent. (b) Since the kernel of A has dimension 1, the image of A has dimension 2, and therefore has a basis consisting of 2 of the c;. Which two make a basis of the image of A?
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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![Suppose that A = [c, c2 C3] is a 3 × 3 matrix with columns c;, and suppose that a basis for the kernel
1
of A is given by the vector
(a) Write and circle an equation involving the c; that shows that the c; are not linearly independent.
(b) Since the kernel of A has dimension 1, the image of A has dimension 2, and therefore has a basis
consisting of 2 of the c;. Which two make a basis of the image of A?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F704a64b5-5250-41d0-9c29-5aaf5a50e535%2Fc81b705c-53aa-4677-acd8-7028793377ee%2Fxl9o5d9_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that A = [c, c2 C3] is a 3 × 3 matrix with columns c;, and suppose that a basis for the kernel
1
of A is given by the vector
(a) Write and circle an equation involving the c; that shows that the c; are not linearly independent.
(b) Since the kernel of A has dimension 1, the image of A has dimension 2, and therefore has a basis
consisting of 2 of the c;. Which two make a basis of the image of A?
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