Q. 63.7( 27 Votes )

Find the values of x, y, z if the matrix satisfy the equation A’A =I.

Answer :

Given A

Transpose of a matrix: If A be an m×n matrix, then the matrix obtained by interchanging the rows and columns of A is called the transpose of A. It is denoted by A’ or AT.


Transpose of A = A’ =


Given equation


A’A =I


=



=


. =


As these matrices are equal to each other that means each element of matrix on L.H.S is equal each element of matrix on R.H.S.


On comparing elements on both sides we get


4y2 + z2 = 1 …… (1)


2y2 – z2 = 0 …… (2)


x2 + y2 + z2 = 1 …… (3)


– y2 – z2 = 0 …… (4)


From equation (4) we get,


x2 = y2 + z2 …… (5)


Substituting this value in equation (3) we get,


2y2 + 2z2 = 1 …… (6)


Subtracting equation (2) and (6) we get,


3z2 = 1


z2 = 1/3


z = 1/3


Substituting value of z in equation (2) we get,


2y2 = 1/3


y2 = 1/6


y = �1/6


Substituting values of y and z in equation (5) we get,



x2 = 1/2


x = 1/2


Hence values of x, y, z are 1/2, 1/6, 1/3 respectively.

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 matricesTriangular Matrices & operations on matricesTriangular Matrices & operations on matrices58 mins
Determinants of Matrices of different orderDeterminants of Matrices of different orderDeterminants of Matrices of different order59 mins
Types of Matrices & PropertiesTypes of Matrices & PropertiesTypes of Matrices & Properties51 mins
Determining a determinantDetermining a determinantDetermining a determinant63 mins
Know About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of Matrix46 mins
Test Yourself, Properties of DeterminantsTest Yourself, Properties of DeterminantsTest Yourself, Properties of Determinants30 mins
Interactive Quiz on Matrices & DeterminantsInteractive Quiz on Matrices & DeterminantsInteractive Quiz on Matrices & Determinants48 mins
Interactive Quiz on Properties of DeterminantsInteractive Quiz on Properties of DeterminantsInteractive Quiz on Properties of Determinants43 mins
Lecture on Product of DeterminantsLecture on Product of DeterminantsLecture on Product of Determinants58 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
caricature
view all courses