Matrices And Matrix Operations
2. Solve the following matrix equation for a, b, c, and d.
a−3d = 2 and a−2d = 3. Therefore, a = 5, b = −3, c = 4, and d = 1
3.
(e) Impossible
(i) tr(D) = 5
(j) tr(D − 3E) = −25
(k) 4tr(7B)=168
(l) undefined
5.
13.
1.4. Inverses; Rules of Matrix Arithmetic
4.
7. In each part, use the given information to find A.
14. Show that if a square matrix A satisfies A2 − 3A + I = 0, then
As we do not know the existence of A−1, we can not use A−1 like
As A2 − 3A + I = 0, I = 3A − A2 =
A(3I − A) and I = 3A − A2 =
(3I − A)A
Therefore, A−1 = 3I − A