Question
Download Solution PDF2x – 3y = 0 and 2x + αy = 0
For what value of α the system has unique solution.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The system of equations A X = 0 is said to be homogenous system of equations, then
If |A| ≠ 0, then its solution X = 0, is called trivial solution.
If |A| = 0. Then A X = 0 has a non-trivial solution which means the system will have infinitely many solutions.
Calculation:
Given: 2x – 3y = 0 and 2x + αy = 0
These equations can be written as: A X = B where
As we know that, the given system is a homogenous system of equation. So, in order to say that the system has unique solution: |A| ≠ 0.
⇒ |A| = 2α + 6 ≠ 0 ⇒ α ≠ -3.
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