Answer :

We are given that,


We need to find the value of x.


Let matrices be,




Then,


Order of A = 1 × 2 [, Matrix A has 1 row and 2 columns]


Order of B = 2 × 2 [, Matrix B has 2 rows and 2 columns]


Since,


Number of columns in A = Number of rows in B = 2


, Order of resulting matrix AB will be 1 × 2.


Resulting matrix = O


O is zero-matrix, where every element of the matrix is zero.


Order of O = 1 × 2


That is,



So,


…(i)


Let,



Let us solve the left hand side of the matrix equation.


In multiplication of matrices,


For z11: Dot multiply 1st row of first matrix and 1st column of second matrix, and then sum up.


(x 1)(1 -2) = x × 1 + 1 × -2


(x 1)(1 -2) = x – 2


So,



For z12: Dot multiply 1st row of first matrix and 2nd column of second matrix, and then sum up.


(x 1)(0 0) = x × 0 + 1 × 0


(x 1)(0 0) = 0 + 0


(x 1)(0 0) = 0


So,



Substituting the resulting matrix in left hand side of (i),



We know by the property of matrices,



This implies,


a11 = b11, a12 = b12, a21 = b21 and a22 = b22


Therefore,


x – 2 = 0


x = 2


Thus, the value of x is 2.


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