Alnico
iron
We need to identify the hard ferromagnetic material among the given options.
Ferromagnetic materials exhibit strong magnetism due to the alignment of atomic magnetic moments within domains.
Alnico alloys are a family of iron alloys which in addition to iron are composed primarily of aluminium (Al), nickel (Ni) and cobalt (Co), hence al-ni-co. They also include copper, and sometimes titanium. Alnico alloys are ferromagnetic, and are used to make permanent magnets. They are hard ferromagnetic materials.
The hard ferromagnetic material among the following is Alnico.
Hard ferromagnetic materials have a high coercivity, meaning they are difficult to demagnetize once magnetized. Among the options, Alnico is the only material that is a hard ferromagnetic material.
Iron, cobalt, and nickel are soft ferromagnetic materials, meaning they can easily be magnetized and demagnetized.
Gadolinium is also a ferromagnetic material but is not as hard as Alnico.
Alnico is an alloy made from aluminum, nickel, and cobalt, and it is known for its high magnetic strength and resistance to demagnetization.
If $ X = A \times B $, $ A = \begin{bmatrix} 1 & 2 \\-1 & 1 \end{bmatrix} $, $ B = \begin{bmatrix} 3 & 6 \\5 & 7 \end{bmatrix} $, find $ x_1 + x_2 $.