(b) Consider the linear system 1 43 +1 73+1 а — В 4о 0 — В 7а 0 where a and ß are real constants. The set of solutions of this system depends on the values of a and B. (i) In the case where a = 0, find all values of 3 for which this system is inconsistent. (ii) In the case where a + 0, find all values of a and 3 for which the set of solutions of this system is a one-dimensional flat in R4. Hence, find in terms of a and 3 a vector parametric equation for this solution flat.

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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Can you help me with question ii (2nd part) please, Thank you!
(b)
Consider the linear system
1
1
3
β 4α 0
β Τα 0
43 +1
73+1
where a and B are real constants. The set of solutions of this system depends on the values of
a and B.
(i) In the case where a = 0, find all values of 3 for which this system is inconsistent.
(ii) In the case where a + 0, find all values of a and B for which the set of solutions of this
system is a one-dimensional flat in R4.
Hence, find in terms of a and B a vector parametric equation for this solution flat.
Transcribed Image Text:(b) Consider the linear system 1 1 3 β 4α 0 β Τα 0 43 +1 73+1 where a and B are real constants. The set of solutions of this system depends on the values of a and B. (i) In the case where a = 0, find all values of 3 for which this system is inconsistent. (ii) In the case where a + 0, find all values of a and B for which the set of solutions of this system is a one-dimensional flat in R4. Hence, find in terms of a and B a vector parametric equation for this solution flat.
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