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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