Respuesta :
Answer:
The value of AB is [tex]\left[\begin{array}{ccc}21\\11\end{array}\right][/tex] and it's not possible to multiply BA.
Step-by-step explanation:
Consider the provided matrices.
[tex]A=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right][/tex], [tex]B=\left[\begin{array}{ccc}3\\5\end{array}\right][/tex]
Two matrices can be multiplied if and only if first matrix has an order m × n and second matrix has an order n × v.
Multiply AB
Matrix A has order 2 × 2 and matrix B has order 2 × 1. So according to rule we can multiply both the matrix as shown:
[tex]AB=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right] \left[\begin{array}{ccc}3\\5\end{array}\right][/tex]
[tex]AB=\left[\begin{array}{ccc}2\times 3+3\times 5\\2\times 3+1\times 5\end{array}\right][/tex]
[tex]AB=\left[\begin{array}{ccc}6+15\\6+5\end{array}\right][/tex]
[tex]AB=\left[\begin{array}{ccc}21\\11\end{array}\right][/tex]
Hence, the value of AB is [tex]\left[\begin{array}{ccc}21\\11\end{array}\right][/tex]
Now calculate the value of BA as shown:
Multiply BA
Matrix B has order 2 × 1 and matrix A has order 2 × 2. So according to rule we cannot multiply both the matrix.
We can multiply two matrix if first matrix has an order m × n and second matrix has an order n × v.
That means number of column of first matrix should be equal to the number of rows of second matrix.
Hence, it's not possible to multiply BA.
