Question

please help it's urgent ​

Answer 1

$\large\underline{\sf{Solution-}}$

Let the required matrix be A whose order is 2 × 3 is

$\begin{gathered}\rm :\longmapsto\:\rm Let\:A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{array}\right]\end{gathered}$

Now,

According to statement,

$\rm :\longmapsto\:a_{ij} \: = \: \dfrac{1}{2} \: |i - 2j|$

So,

$\rm :\longmapsto\:a_{11} \: = \: \dfrac{1}{2} \: |1 - 2| = \dfrac{1}{2}$

$\rm :\longmapsto\:a_{12} \: = \: \dfrac{1}{2} \: |1 - 4| = \dfrac{3}{2}$

$\rm :\longmapsto\:a_{13} \: = \: \dfrac{1}{2} \: |1 - 6| = \dfrac{5}{2}$

$\rm :\longmapsto\:a_{21} \: = \: \dfrac{1}{2} \: |2 - 2| = \dfrac{0}{2} = 0$

$\rm :\longmapsto\:a_{22} \: = \: \dfrac{1}{2} \: |2 - 4| = \dfrac{2}{2} = 1$

$\rm :\longmapsto\:a_{23} \: = \: \dfrac{1}{2} \: |2 - 6| = \dfrac{4}{2} = 2$

Hence,

$\begin{gathered}\rm :\longmapsto\:\rm \:A=\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{3}{2} &\dfrac{5}{2} \\ \\ 0&1&2\end{array}\right]\end{gathered}$

Additional Information :-

1. Addition of two matrices A and B is possible only when order of A and B is same.

2. Subtraction of two matrices A and B is possible only when order of A and B is same.

3. Matrix multiplication is possible only when number of columns of pre multiplier is equals to number of rows of post multiplier.

Answer 2

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