Question

A) arătați ca det.(A(1)+A(2)+A(3)=9
B)determinati inversa matricei A(4)
C) Calculati det(A(1)+A(2)+... A(100)
OFER TOATE PUNCTELE​

Answer 1

Explicație pas cu pas:

A)

det(A(1)+A(2)+A(3)) = 3×3 - 0×(-2-4-6) = 9

B)

A(4) = [(1;-2×4);(0;1)] = [(1;-8);(0;1)]

det(A(4)) = 1×1-0×(-8) = 1 ≠0

tA = [(1;0);(-8;1)]

A* = [(1;-(-8));(-0;1)] = [(1;8);(0;1)]

A^{-1} = 1/1 × A* = [(1;8);(0;1)]

C)

det((A(1)+A(2)+... A(100)) = 100×100-0×(-2×1-2×2-...-2×100) = 10⁴