Question

Find the value of m, n, p, q


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

Answer 1

Given Question :-

Find the value of m, p, n and q.

$\rm :\longmapsto\:5\begin{bmatrix} 3 & 4\\ - 9 & - 1\end{bmatrix} = \begin{bmatrix} m & p\\ n & q\end{bmatrix}$

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

Given matrix equation is

$\rm :\longmapsto\:5\begin{bmatrix} 3 & 4\\ - 9 & - 1\end{bmatrix} = \begin{bmatrix} m & p\\ n & q\end{bmatrix}$

can be rewritten as

$\rm :\longmapsto\:\begin{bmatrix} 15 & 20\\ - 45 & - 5\end{bmatrix} = \begin{bmatrix} m & p\\ n & q\end{bmatrix}$

We know,

Two matrices A and B are equal iff

↝ 1. They have same order

↝ 2. Corresponding elements are same.

Since, matrices are equal

So, on comparing, we get

$\red{\rm :\longmapsto\:m = 15}$

$\red{\rm :\longmapsto\:p = 20}$

$\red{\rm :\longmapsto\:n \: = - \: 45}$

$\red{\rm :\longmapsto\:q \: = - \: 5}$

More to know :-

1. Order of a matrix is defined as product of number of rows × number of columns.

2. Order gives the following information :

(a) Number of elements in a matrix.

(b) Number of elements in each row

(c) Number of elements in each column.

3. Matrix multiplication is defined when number of columns of pre multiplier is equals to number of rows of post multiplier otherwise matrix multiplication is not defined.

4. Matrix multiplication may or may not be Commutative.

5. Matrix multiplication is Associative.

6. Matrix multiplication is Distributive.