Question

$\begin{gathered} \bold{G = \begin{bmatrix}1 & 2 \\3 & 4 \\ 6 &7\end{bmatrix}}\end{gathered}$

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$\bold{Element \: G_{22} \: is}$




❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ
❖ ɴᴏ ꜱᴘᴀᴍᴍɪɴɢ
❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​​​​​​​​​​​​​​​​​​​​​

Answer 1

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

Given matrix is

$\rm :\longmapsto\:G =\begin{gathered} \bold{ \begin{bmatrix}1 & 2 \\3 & 4 \\ 6 &7\end{bmatrix}}\end{gathered}$

We know,

$\rm :\longmapsto\:In \: a \: matrix \: a_{ij} \: represents \: element \: of \: {i}^{th} \: row \: and \: \\ \rm \: {j}^{th} \: column \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So,

$\rm :\longmapsto\:G_{22} \: represents \: element \: of \: {2}^{nd} \: row \: and \:{2}^{nd} \: column$

So, in given matrix

$\rm :\longmapsto\:G =\begin{gathered} \bold{ \begin{bmatrix}1 & 2 \\3 & 4 \\ 6 &7\end{bmatrix}}\end{gathered}$

we have

$\red{\rm :\longmapsto\:G_{11} = 1}$

$\red{\rm :\longmapsto\:G_{12} = 2}$

$\red{\rm :\longmapsto\:G_{21} = 3}$

$\red{\rm :\longmapsto\:G_{22} = 4}$

$\red{\rm :\longmapsto\:G_{31} = 6}$

$\red{\rm :\longmapsto\:G_{32} = 7}$

Hence,

$\rm \implies\:\boxed{ \tt{ \: G_{22} \: = \: 4 \: }}$

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Explore more :-

1. Order of a matrix is defined as number of rows × number of columns. Order provides the following information :

• Number of elements in each row

• Number of elements in each column

• Number of elements in matrix.

2. Matrix addition is possible only when order of both matrices is same.

3. Matrices Subtraction is possible only when order of both the matrices are same.

4. Matrix multiplication is defined when number of columns of pre multiplier is equal to the number of rows of post multiplier.

5. Matrix multiplication may or may not be Commutative.

6. Matrix multiplication is Associative.

7. Matrix multiplication is Distributive.