SpletIf , show that A2– 5A + 7I = O. Hence find A–1. We have A2= A.A = . So A2– 5A + 7I = Hence A2– 5A + 7I = 0 ∴A.A – 5A = -7I Now post multiply with A-1 So A.A.A-1-5A.A-1= -7I.A-1 … SpletCayley Hamilton theorem states that the characteristic equation is satisfied by A ∴ Replacing λ with A ∴ A 2 − 4 A − 5 I = 0 -------- (2) Given : A 5 − 4 A 4 − 7 A 3 + 11 A 2 − A − 10 I ------ (3) ∴ Dividing Equation (3) by Equation (2)

Ex 3.3, 4 - Find (A + 2B)

Splet05. mar. 2024 · Best answer We have, A = [ 2 −3 3 4] A = [ 2 − 3 3 4] Hence, matrix A satisfies the equation, x2 - 6x +17 Now, A2 - 6A + 17I2 = 0 ⇒ A2 - 6A = -17I2 Multiplying … SpletNow, A 2−4A+7I=[ 1−4121]−4[ 2−132]+7[1001] = [ 1−4121]−[ 8−4128]+[7007]=[0000]=0(zeromatrix) ⇒ A 2−4A+7I=0 ⇒ A 2=4A−7I. ⇒ A⋅A 2=4A⋅A−7AI … bj jayeonii

If A = 3 1 - 1 2 , show that A^2 - 5A + 7I = 0. Hence, find A^-1. - Toppr

SpletAnswer: If A3 −A2 +A−I= 0, then (A2 −A+I)A= A3 −A2 +A= I= A3 −A2 +A= A(A2 −A+I) so A−1 = A2 −A+I. ♣ (b): If Ais a square matrix satisfying A7 = 0, find (I−A)−1 in terms of A. … SpletYou have to show that any matrix that satisfies the equation A 2 + 2 A + I = 0 is invertible. – 5xum Mar 2, 2014 at 22:49 Add a comment 5 Answers Sorted by: 4 The inverse of A is almost certainly not A. You have A 2 + 2 A = − I, or A ( A + 2 I) = − I. Multiplying by − 1 you get A ( − A − 2 I) = I Hence the inverse of A is − A − 2 I. Share Cite Splet30. avg. 2024 · Best answer We have, Therefore, A2 – 4A + 7I A2 = 4A – 7I Thus A3 = A.A2 = A (4A – 7I) = 4 (4A – 7I) – 7A = 16A – 28I – 7A = 9A – 28I and so A5 = A3A2 = (9A – … linen\\u0027s vn