Q. 584.0( 3 Votes )

# If <img wid

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 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