Construct a 2 - 2 matrix whose elements are a ij -1-2 2 i -3 j

A=[ a_11 amp;a_12; a_21 amp;a_22 ] a_11=1/2[2(1) 3(1)]= 1/2 a_12=1/2[2(1) 3(2)]= 4/2= 2 a_21=1/2[2(2) 3(1)]=1/2 a_22=1/2[2(2) 3(2)]= 2/2= 1 Therefore A= ...

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Standard X

Mathematics

Matrix Definition and Representation

Construct a 2...

Question

Construct a 2 $\times$ 2 matrix whose elements are $a_{i j}$ = $\frac{1}{2}$ (2i – 3j)

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Solution

A= $[\begin{matrix} a_{11} & a_{12} a_{21} & a_{22} \end{matrix}]$

$a_{11} = \frac{1}{2} [2 (1) - 3 (1)] = - \frac{1}{2}$
$a_{12} = \frac{1}{2} [2 (1) - 3 (2)] = - \frac{4}{2} = - 2$
$a_{21} = \frac{1}{2} [2 (2) - 3 (1)] = \frac{1}{2}$
$a_{22} = \frac{1}{2} [2 (2) - 3 (2)] = - \frac{2}{2} = - 1$

Therefore $A = ⎡ ⎣ \begin{matrix} \frac{- 1}{2} & - 2 \frac{1}{2} & - 1 \end{matrix} ⎤ ⎦$

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Construct a 2 × 2 matrix whose elements are aij=12 (2i – 3j)

A=[a11a12a21a22] a11=12[2(1)−3(1)]=−12 a12=12[2(1)−3(2)]=−42=−2 a21=12[2(2)−3(1)]=12 a22=12[2(2)−3(2)]=−22=−1 Therefore A=⎡⎣−12−212−1⎤⎦

Construct a 2 $\times$ 2 matrix whose elements are $a_{i j}$ = $\frac{1}{2}$ (2i – 3j)