[ 2'5 puntos] . Resuelve la ecuación matricial A^2× X = 2B, siendo A = y B =.

A^2× X = 2B,

A = y B =

Como |A| = = - 3 + 2 = - 1 ¹ 0, la matrtiz A tiene inversa A ^-1

(A²) ^-1× A² × X = (A²) ^-1× 2× B = 2× (A²) ^{-1 ×} B ® X = 2× (A²) ^{-1 ×} B

A² =× =

| A²| = |A| × |A| = (-1)(-1) = +1

(A²) ^-1 =× Adj (A²) ^t

(A²) ^t = ® Adj (A²) ^t = ® (A²) ^-1 =× Adj (A²) ^t =

X = 2× (A²) ^{-1 ×} B = 2× × = 2× =