Find the value of x for which the matrix product
Find the value of x for which the matrix product

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 441

Solution:

We know,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 442

is identity matrix of size

    \[3\]

So according to the given criteria

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 443

Now we will multiply the two matrices on LHS using the formula

    \[{{c}_{ij}}~=\text{ }{{a}_{i1}}{{b}_{1j}}~+\text{ }{{a}_{i2}}{{b}_{2j}}~+\text{ }\ldots \text{ }+\text{ }{{a}_{in~}}{{b}_{nj}},\]

 we get

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 444

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 445

And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal

So we get

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 446

So the value of

    \[x\]

is
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 447