Matrices and Determinants 1 Question 1

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1. If A is a symmetric matrix and B is a skew-symmetric matrix such that A+B=23 51, then AB is equal to

======= ####1. If A is a symmetric matrix and B is a skew-symmetric matrix such that A+B=[2351], then AB is equal to

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed

(a) [4214]

(b) [4214]

(c) [4214]

(d) [4214]

(2019 Main, 12 April I)

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Answer:

Correct Answer: 1. (b)

Solution:

  1. Given matrix A is a symmetric and matrix B is a skew-symmetric.

AT=A and BT=B

Since, A+B=[2351] (given)… (i)

On taking transpose both sides, we get

(A+B)T=[23 51] AT+BT=[25 31]

Given, AT=A and BT=B

AB=[25 31]

On solving Eqs. (i) and (ii), we get

A=[24 41] and B=[01 10]  So, AB=[2401 4110]=[42 14]



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