Question

Can you multiply the \[2\times2\] matrix by a \[3\times3\] matrix ?

Answer 1

Hint: In this question, we need to explain whether the multiplication of the matrix \[2\times2\] and \[3\times3\] is possible or not. Matrix is nothing but a rectangular array of numbers or symbols arranged in rows and columns . The product of the two matrices produces a single matric . It is also known as a matrix product. If a matrix has \[x\] rows and \[y\] columns, then the order of the matrix is \[x\times y\] . First, we need to check the number of rows and columns of the two given matrices. Then we need to check whether the number of columns in the first matrix is equal to the number of rows in the second matrix .
Matrix multiplication :
If \[A\] and \[B\] are the two matrices, then the product of the two matrices is,
\[X = AB\]
Therefore the product of two matrices is the dot product of the two matrices.

Complete answer:
Given , \[2\times2\] matrix and \[3\times3\] matrix.
Here , the first number represents the number of rows and similarly the second number represents the number of columns.
The most important condition in the multiplication of the matrix is that the number of columns in the first matrix is equal to the number of rows in the second matrix. The resultant matrix will have the number of rows in the first matrix and the number of columns in the second matrix.
Here the number of columns in the first matrix is \[2\] and the number of rows in the second matrix is \[3\] .
Clearly the number of columns in the first matrix is not equal to the number of rows in the second matrix.
From this, we can conclude that we can’t multiply the \[2\times2\] matrix by a \[3\times3\] matrix.
Final answer :
We can’t multiply the \[2\times2\] matrix by a \[3\times3\] matrix.

Note:
Matrix performs various operations such as addition, subtraction, multiplication , division and so on. Multiplying the matrix by a single number is known as scalar multiplication. Mathematically, The product of two matrices \[A\] and \[B\] is defined if the number of columns of \[A\] is equal to the number of rows of \[B\] . The order of the resulting matrix is known as the matrix multiplication order. Matrices are classified into many types depending on the order and the elements.