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Choose the correct answer in the Exercises 11 and 12.

Q12.    If  and , then the value of  is

(A)

(B)

(C)

(D)

Option B is correct.

Choose the correct answer in the Exercises 11 and 12.

Q11.    If A, B are symmetric matrices of same order, then AB – BA is a

(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix

If A, B are symmetric matrices then                                                          and       we have,                                                                                                                                                                                                                                 Hence, we have  Thus,( AB-BA)' is skew symmetric. Option A...

Q10.    Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(iv)

Let                       Thus,    is a symmetric matrix.                Let  Thus,  is a skew-symmetric matrix. Represent   A  as the sum of B and C.

Q10.    Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(iii)

Let                       Thus,    is a symmetric matrix.                Let  Thus,  is a skew-symmetric matrix. Represent   A  as the sum of B and C.

Q10.    Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(ii)

Let                       Thus,    is a symmetric matrix.                Let  Thus,  is a skew-symmetric matrix. Represent   A  as the sum of B and C.

10.    Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i)

Let                       Thus,    is a symmetric matrix.                Let  Thus,  is a skew symmetric  matrix. Represent   A  as sum of B and C.

Q9.    Find  and , when

the transpose of the matrix is obtained by interchanging rows and columns

Q8.    For the matrix , verify that

(ii)  is a skew symmetric matrix.

We have  Hence ,   is a skew-symmetric matrix.

Q8.    For the matrix , verify that

(i)  is a symmetric matrix.

We have  Hence ,   is a symmetric matrix.

Q7.    (ii) Show that the matrix is a skew-symmetric matrix.

The transpose of A is Since, so given matrix is a skew-symmetric matrix.

Q7.    (i) Show that the matrix  is a symmetric matrix.

the transpose of A is Since, so given matrix is a symmetric matrix.

Q6.    (ii) If , then verify that

By interchanging columns and rows of the matrix A we get the transpose of A To prove:  L.H.S :

Q6.    (i) If , then verify that

By interchanging rows and columns we get transpose of A To prove:  L.H.S :

Q5.    For the matrices A and B, verify that , where

(ii)

,  To prove :  Heence, L.H.S =R.H.S  i.e..

Q5.    For the matrices A and B, verify that , where

(i)

,     To prove :  Hence, L.H.S =R.H.S  so it is verified that .

Q4.    If  and , then find

: Transpose is obtained by interchanging rows and columns and the transpose of A+2B is

Q3.    If  and , then verify

(ii)

To prove:        R.H.S:      Hence, L.H.S = R.H.S i.e. .

Q3.    If   and , then verify

(i)

To prove:

R.H.S:

Hence, L.H.S = R.H.S, hence verified that .

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Q2.    If  and , then verify

(ii)

and        L.H.S :        R.H.S :      Hence, L.H.S = R.H.S. so verified that   .

Q2.    If  and , then verify

(i)

and        L.H.S :        R.H.S :      Thus we find that the LHS is equal to RHS and hence verified.
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