You visited us 1 times! Enjoying our articles? Unlock Full Access!

Multiplication of Matrices

Suppose a Mat...

Question

Suppose a Matrix A satisfies $A^{2} - 5 A + 7 I = 0. I f A^{5} = a A + b I$ , then the values of $2 a + b i s .$

- 87

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- 105

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1453

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1155

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A - 87
$A^{3} = A A^{2} = A (5 A - 7 I) = 5 A^{2} - 7 A (5 A - 7 I) - 7 A = 18 A - 35 I A^{4} = A . A^{3} = A (18 A - 35 I) = 18 (5 A - 7 I) - 35 A A^{5} = 149 A - 385 I = 55 A - 126 I A^{5} = 149 A - 385 I a = 149, b = - 385$

Suggest Corrections

Similar questions

A^{2} - 5 A + 7 I = 0

A^{5} = a A + b I

A

A^{2} - 5 A + 7 I = 0

A^{8} = a A + b I

a =

A

A^{2} - 5 A + 7 I = 0

A^{8} = a A + b I

a

A = [\begin{matrix} 3 & 2 1 & 1 \end{matrix}],

^{'} a^{'}

^{'} b^{'}

A^{2} + a A + b I = 0

A = [\begin{matrix} 3 & 2 1 & 1 \end{matrix}],

A^{2} + a A + b I = O

(a, b)

Join BYJU'S Learning Program