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ohaa [14]
3 years ago
15

A= [2, 3; 2, 1], B=[3; 5]. Find AB & BA if possible

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
5 0

Answer:

The value of AB is \left[\begin{array}{ccc}21\\11\end{array}\right] and it's not possible to multiply BA.

Step-by-step explanation:

Consider the provided matrices.

A=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right], B=\left[\begin{array}{ccc}3\\5\end{array}\right]

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:

AB=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right] \left[\begin{array}{ccc}3\\5\end{array}\right]

AB=\left[\begin{array}{ccc}2\times 3+3\times 5\\2\times 3+1\times 5\end{array}\right]

AB=\left[\begin{array}{ccc}6+15\\6+5\end{array}\right]

AB=\left[\begin{array}{ccc}21\\11\end{array}\right]

Hence, the value of AB is \left[\begin{array}{ccc}21\\11\end{array}\right]

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.

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