Q. 224.2( 5 Votes )

If find the value of a and b such that A2 + aA + bI = O.

Answer :

Given : A2 + aA + bI = O


A is a matrix of order 2 x 2


To find : a and b


Formula used :



Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj


If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c


A2 is a matrix of order 2 x 2


A2 = = =


A2 =


aA = a =


bI = b =


bI =


A2 + aA + bI = + + =


A2 + aA + bI =


It is given that A2 + aA + bI = 0


=


Equating similar terms in the matrices,we get


4 + a = 0 and 3 + a + b = 0


a = 0 – 4 = -4


a = -4


substituting a = -4 in 3 + a + b = 0


3 – 4 + b = 0


-1 + b = 0


b = 0 + 1 = 1


b = 1


a = -4 and b = 1


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Triangular Matrices & operations on matrices58 mins
Determinants of Matrices of different order59 mins
Types of Matrices & Properties51 mins
Determining a determinant63 mins
Lecture on Product of Determinants58 mins
Interactive Quiz on Properties of Determinants43 mins
Know About finding the Adjoint & Inverse Of Matrix46 mins
Test Yourself, Properties of Determinants30 mins
Interactive Quiz on Matrices & Determinants48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses