Question

If A is of order $m\times n$, B is of order $3\times p$ and C is of order $2\times 4$. If AB+C is defined ,find m ,n and p.

Answer 1

Hint:In such a type of question the solution should be divided in two parts, first multiplication of two matrices and when it's possible . Second addition of matrix and when it's possible and try to get the answer.

Complete step-by-step answer:
Given definition is AB+C and we can write it with its order like that
${{A}_{m\times n}}{{B}_{3\times p}}+{{C}_{2\times 4}}$ ………………………….(i)
Now matrix A is multiplied with matrix B.
We know that the product of two matrices is defined , if the number of columns of A is equal to the number of rows of B.
Here ${{A}_{m\times n}}$ has m columns and n rows.
Similarly ${{B}_{3\times p}}$has 3 columns and p rows .
From the rule of multiplication of matrix column of A is equal or row of A is equal to row of B or column of B. So that $n=3$
So that equation (i) is in the form of
$A{{B}_{m\times p}}+{{C}_{2\times 4}}$
Addition of any two matrix is possible when they are in same order it means
 $m\times p=2\times 4$
On comparison we get,
$m=2\,and\,p=4$
Hence the values of $m = 2,n = 3{\text{ and }}p = 4$

Note:A matrix is an ordered rectangular array of numbers.Suppose a matrix has m rows and n columns, then the order of matrix is written as $m\times n$.We should know about when we multiply a matrix to other such that if number of rows is not equal to number of columns of the other matrix then product is not possible. Similarly for the addition or subtraction order should be the same .