Construct a 3 × 2 matrix whose elements are given

Question:

Construct a $3 \times 2$ matrix whose elements are given by $a_{i j}=(2 i-j)$.

 

Solution:

Given: $a_{i j}=(2 i-j)$

Now, $a_{11}=(2 \times 1-1)=2-1=1$

$a_{12}=2 \times 1-2=2-2=0$

$a_{21}=2 \times 2-1=4-1=3$

$a_{22}=2 \times 2-2=4-2=2$

$a_{31}=2 \times 3-1=6-1=5$

$a_{32}=2 \times 3-2=6-2=4$

Therefore,

$A=\left[\begin{array}{ll}1 & 0 \\ 3 & 2 \\ 5 & 4\end{array}\right]$

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