Q. 495.0( 7 Votes )

Find a 2 × 2 matr

Answer :

Given A is a 2×2 matrix,


So let


Here I2 is an identity matrix of size 2,


So the given equation becomes,





To satisfy the above equality condition, corresponding entries of the matrices should be equal, i.e.,


a + b = 6…….(i)


– 2a + 4b = 0 2a = 4b a = 2b……..(ii)


c + d = 0 c = – d……(iii)


– 2c + 4d = 6 ……(iv)


Substitute the values of eqn(ii) in eqn (i), we get


a + b = 6 2b + b = 6 b = 2


So eqn(ii) becomes, a = 2b = 2(2) = 4 a = 4


Substitute the values of eqn(iii) in eqn (iv), we get


– 2c + 4d = 6 – 2( – d) + 4d = 6 2d + 4d = 6 6d = 6 d = 1


So eqn(iii) becomes, c = – d c = – 1


Now substituting these values in matrix A, we get


is the matrix A.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

Using matrices, sMathematics - Board Papers

If possible, usinMathematics - Exemplar

If possible, usinMathematics - Exemplar

Using matrices, sMathematics - Board Papers

Prove that <span Mathematics - Board Papers

Find the value ofMathematics - Board Papers

If A is a <span lMathematics - Board Papers