Solve Problems A.1 through A.6 using matrices [A], [B], [C], [D], and {E} given by...

Solve Problems A.1 through A.6 using matrices [A], [B], [C], [D], and {E} given by

(Write ‘‘nonsense’’ if the operation cannot be performed.)

The following integral represents the strain energy in a bar of length L and crosssectional area A:

and E is the modulus of elasticity.

Show that dU/d{d} yields [k]{d}, where {k} is the bar stiffness matrix given by