Consider the matrices [2 0 -1] D = |1 4 2 -1 0 1 1 0 3 A В 3 and F = |0 5 4 2 2 (a) Show that A, B, C, D and F are invertible matrices. (b) Solve the following equations for the unknown matrix X. (i)...

Extracted text: Consider the matrices [2 0 -1] D = |1 4 2 -1 0 1 1 0 3 A В 3 and F = |0 5 4 2 2 (a) Show that A, B, C, D and F are invertible matrices. (b) Solve the following equations for the unknown matrix X. (i) AXT = BC³, (ii) A-'(X – 1)" = (B-!)", (iii) XF = F¯1 – D". %3D %3D Let H and G be subspaces of a vector space V. Show that HNG is a subspace of V. (Note that the intersection of H and G, written as H NG, is the set of vectors v E V that belong to both H and G).