$3 \times 4$ શ્રેણિકના સભ્યો $a_{i j}=2 i-j$ દ્વારા મળે, તો તે શ્રેણિકની રચના કરો.

Question

A$A=\left[\begin{array}{cccc}-1 & 0 & -1 & -2 \\ 3 & 2 & 1 & 0 \\ -5 & 4 & 3 & 2\end{array}\right]$
B$A=\left[\begin{array}{cccc}1 & 0 & -1 & -2 \\ 3 & 2 & 1 & 0 \\ 5 & 4 & 3 & 2\end{array}\right]$
C$A=\left[\begin{array}{cccc}1 & 0 & -1 & 2 \\ 3 & 2 & 1 & 0 \\ 5 & -4 & -3 & 2\end{array}\right]$
D$A=\left[\begin{array}{cccc}1 & 0 & 1 & 2 \\ 3 & 2 & 1 & 0 \\ 5 & -4 & 3 & 2\end{array}\right]$

Medium

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Solution

$a_{i j}=2 i-j$, $i=1,\,2,\,3$ and $j=1,\,2,\,3,\,4$

Thus, we have

$a_{11}=2 \times 1-1=2-1=1$

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

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

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

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

$a_{12}=2 \times 3-2=6-2=4$

$a_{13}=2 \times 1-3=2-3=-1$

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

$a_{13}=2 \times 3-3=6-3=3$

$a_{14}=2 \times 1-4=2-4=-2$

$a_{24}=2 \times 2-4=4-4=0$

$a_{14}=2 \times 3-4=6-4=2$

Therefore, the required matrix is $A=\left[\begin{array}{cccc}1 & 0 & -1 & -2 \\ 3 & 2 & 1 & 0 \\ 5 & 4 & 3 & 2\end{array}\right]$

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