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Question
Examine the consistency of the system of equations.
x + 3y = 5
2x + 6y = 8
Solution
Let, A `= [(1,3),(2,6)], X = [(x),(y)], B = [(5),(8)]`
Then the given system of equations can be written as,
`[(1,3),(2,6)][(x),(y)] = [(5),(8)]`
Now, `abs A = [(1,3),(2,6)] = 1 xx 6 - 2 xx 3 = 0`
cofactors of the elements of `abs A` are respectively
`A_11 = 6, A_12 = -2, A_21 = -3, A_22 = 1`
`therefore adj A = [(6,-2),(-3,1)] = [(6,-3),(-2,1)]`
`=> (adj A) B = [(6,-3),(-2,1)] [(5),(8)] = [(30 - 24),(-10 + 8)] = [(6),(-2)] ne 0`
`abs A = 0 और (adj A) "B" ne 0`
Therefore, the given system of equations is inconsistent.
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