Question

if A=(aij)2*3 is a matrix such that aij 1÷2 [i-2j] then a12 1\2 a23 is equal to

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Answer 1

SOLUTION

GIVEN

$\sf{A =( a_{ij} ) \: is \: a \: 2 \times 3 \: \: matrix \: such \: that }$

$\displaystyle \sf{a_{ij} = \frac{1}{2}(i - 2j) }$

TO DETERMINE

$\displaystyle \sf{a_{12} \: \: and \: \: a_{23}}$

EVALUATION

Here it is given that

$\sf{A =( a_{ij} ) \: is \: a \: 2 \times 3 \: \: matrix \: such \: that }$

$\displaystyle \sf{a_{ij} = \frac{1}{2}(i - 2j) }$

Now

$\displaystyle \sf{a_{11} = \frac{1}{2}(1- 2) = - \frac{1}{2} }$

$\displaystyle \sf{a_{12} = \frac{1}{2}(1 - 4) = - \frac{3}{2} }$

$\displaystyle \sf{a_{13} = \frac{1}{2}(1- 6) = - \frac{5}{2} }$

$\displaystyle \sf{a_{21} = \frac{1}{2}(2- 2) = 0}$

$\displaystyle \sf{a_{22} = \frac{1}{2}(2 - 4) = - 1 }$

$\displaystyle \sf{a_{23} = \frac{1}{2}(2- 6) = - 2}$

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