2. Suppose a certain system of equations Ar = b has a solution set which can be written in the following parametric vector form (with free parameters c and c2): 1 + c1 0. + c2 1 1 (a) What is the rank of A? (b) Find a basis for Nul A, the null space of A. Find a matrix B so that all x E (Nul A) satisfy Bx = 0 and use this to find a basis for (c) (Nul A).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Suppose a certain system of equations Ax b has a solution set which can be written in the following
parametric vector form (with free parameters ci and c2):
1
+ ci
C2
1
(a)
What is the rank of A?
(b)
Find a basis for Nul A, the null space of A.
Find a matrix B so that all x € (Nul A) satisfy Bx 0 and use this to find a basis for
(c)
(Nul A)-.
Transcribed Image Text:2. Suppose a certain system of equations Ax b has a solution set which can be written in the following parametric vector form (with free parameters ci and c2): 1 + ci C2 1 (a) What is the rank of A? (b) Find a basis for Nul A, the null space of A. Find a matrix B so that all x € (Nul A) satisfy Bx 0 and use this to find a basis for (c) (Nul A)-.
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