DeterminantHard
Question
If A = 
(where bc ≠ 0) satisfies the equations x2 + k = 0, then
(where bc ≠ 0) satisfies the equations x2 + k = 0, then Options
A.a + d = 0
B.k = - |A|
C.k = |A|
D.none of these
Solution
A = 
bc ≠ 0
Characteristic equation is = 0
= 0
(a - x) (d - x) - bc = 0
x2 - x (a + d) + ad - bc = 0
On comparing with the given equation x2 + k = 0
a + d = 0, k = ad - bc = |A|
bc ≠ 0Characteristic equation is = 0
= 0(a - x) (d - x) - bc = 0
x2 - x (a + d) + ad - bc = 0
On comparing with the given equation x2 + k = 0
a + d = 0, k = ad - bc = |A|
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