Solve the following system of linear equations using LU decomposition. Show each step, including the decomposition process, forward and backward substitutions, and verification of solutions.(I) x1 + x2 + x3 = 13, (II) x1 - x2 + x3 = 6, (III) x1 + x2 - x3 = -3: a. Derive a rate equation for the decomposition of ozone assuming Step 1 is fast and reversible.

Hexagonal space lattice ( From Charles Kittel Introduction to Solid State Physics The vectors of primitive translations of the hexagonal space tattice can be chosen as follows. a = 3 a a a + + e = c z 2 2 2 Show using a formula V= /abx el, that the volume of a primitive cell isv ( 13/2) a c. is equal