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CBSE Class 12 · 2016 · MatricesVery Short Answer

Matrix

A = 03 3 a 2 b 13 - 2 3 - 1

is given to be symmetric; find the values of

a

and

b

.

Answer: $a = - \frac{2}{3}, b = \frac{3}{2}$

Solution

A symmetric matrix satisfies

a_{ij} = a_{j i}

. Match the symmetric pairs:

2 b = 3 \Rightarrow b = \frac{3}{2}, 3 a = - 2 \Rightarrow a = - \frac{2}{3} .

(The pair

a_{23} = a_{32} = 3

is already consistent.)

a = - \frac{2}{3}, b = \frac{3}{2}

CBSE Class 12 Board · 2016 · Subjective

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