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.)

A two-element bar as shown in Figure PA–12 with element lengths L, cross-sectional area A, and Young’s modulus E can be shown to have a stiffness matrix of

Show that the det ([k]) = 0 and hence that [k] is positive semidefinite and the matrix is also singular. Now fix the left end (set u₁ = 0) and show that the reduced [k] is