NCERT Class 12-Mathematics: Exemplar Chapter –3 Matrices Part 7

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Question 12:

Find the matrix A satisfying the matrix equation:

Answer:

We have,

On adding Eqs. (i) and (iv), we get

On adding Eqs. (ii) and (iii), we get

On adding Eqs. (vi) and (iv), we get

From eqs. (v) and (vii)

Now, using the values of a and d in Eq. (iii), we get

Now, using the values of a and d in Eq. (ii), we get

On multiplying Eq. (ix) by 5 and Eq. (x) by 13, then adding, we get

Question 13:

Find A, if

Answer:

Let

Question 14:

If , then verify

Answer:

We have,

And

Also,

So is not possible, since the B is not a square matrix.

Hence,