Differential EquationHard
Question
If A =
is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to :
is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to :Options
A.(2, 1)
B.(-2, -1)
C.(2, -1)
D.(-2, 1)
Solution
= I ⇒ 
is orthogonal matrix
∵ Three rows are corresponding to three mutually perpendicular unit vectors
⇒
= 1, a + 2b + 4 = 0 & 2a − 2b + 2 = 0⇒ a = −2 & b = −1
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