Question

se considera matricele A=(1,2,2,4)si I2=(1,0,0,1) b)arătați ca AxA=5A,c)determinati numerele reale x si y pentru cate A+(×,y,y,-3)=I2​

Answer 1

b) A^2 = AxA =
(1 2 2 4) (1 2 2 4) =
(1+4 2+8 2+8 4+16) =
= (5 10 10 20) = 5(1 2 2 4) = 5A

c) A + B = I2
B = I2 - A
(x y y -3) = (1 0 0 1) - (1 2 2 4)
(x y y -3) = (0 -2 -2 -3)

Sistem:
x = 0
y = -2
y = -2
-3 = -3 (evident)

=> x = 0 si y = -2