Răspuns:
Explicație pas cu pas:
a)
A(2) = (1 0 ) = (1 0 )
(0 2²) (0 4)
det (A(2)) = 1·4 - 0·0 = 4
======================
b) A(3) = (1 0)
(0 8)
A(1) = (1 0)
(0 2)
2A(1) = (2 0)
(0 4)
A(2) = (1 0)
(0 4)
A(3) +2A(2) = (1 0) + (2 0) = (3 0)
(0 8) (0 4) (0 12)
3A(2) = (3 0) = A(3) +2A(2)
(0 12)
=============================
c) A(x) · A(x²) = I₂ ; x = ?
A(x) = (1 0)
(0 2ˣ)
A(x²) = (1 0)
(0 2ˣ²)
A(x) · A(x²) = (1 0) · (1 0) = (1·1+0·0 1·0+0· 2ˣ²) =
(0 2ˣ) (0 2ˣ²) (0·1+2ˣ·0 0· 0+2ˣ· 2ˣ²)
= (1 0 ) = (1 0)
(0 2ˣ²⁺ˣ) (0 1) =>
2ˣ²⁺ˣ = 1 = 2⁰ =>
x²+x = 0 <=> x(x+1) = 0 => x₁ = -1 ; x₂ = 0
