question below:

In Exercises 3-6, find an explicit description of Nul A by listing vectors that span the null space.1 5 -4-3 17 6. A= 01 -2 10 00 0 0 0In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]2. 312 - e21TABLE 7.2 Properties of Laplace Transforms Lift 8 } = L(f } + L(8) . L{ off = CL{f} for any constant c. Leaf ( t ) } (s ) = 2 {f } (s - a) . Eff'} ( s ) = self} (s ) - f(0 ) . {{f" } (s ) = self} (s) - sf (0 ) - f'(0 ). eff (" ) } (s) = s"2{f} (s ) - s"-'f(0) - s"-2f' (0) - ... - f("-1) (0 ) . L{ if ( t) } (s ) = (-1)" ( Self) ( s ) ) .TABLE 7.1 Brief Table of Laplace Transforms f (t ) F (s ) = 2{f} (s) 1 - - , S>0 eat sza s - a 1", n = 1, 2, ... n! S>0 sin bt b 5 2 + 62 ' S>0 S cos bt 52 + 62 ' elli", n = 1, 2, ... n! (s - a)nti ' s > a b ed sin bt (s - a)2+ 62 ' sza s - a e" cos bt (s - a) 2+ 62 ' sza