Question

# Where possible, find the product: begin{bmatrix}2 & 3 &-1&6 0 & 5 &4&1 end{bmatrix} begin{bmatrix}1 & 3 0 & 2 end{bmatrix}

Matrices
Where possible, find the product:
$$\begin{bmatrix}2 & 3 &-1&6 \\ 0 & 5 &4&1 \end{bmatrix} \begin{bmatrix}1 & 3 \\0 & 2 \end{bmatrix}$$

2020-12-31
Step 1
Known facts:
Let A be $$m \times n$$ matrix and B be $$p \times q$$ matrix then the product of these two matrices are defined only when n=p.
That is, Product of two matrices A and B is defined only when number of columns of A is equal to number of rows of B.
Step 2
Note that given matrices order are $$2 \times 4$$ and $$2 \times 2$$. Clearly, $$4 \neq 2$$.
By the above known fact, the product $$\begin{bmatrix}2 & 3 &-1&6 \\ 0 & 5 &4&1 \end{bmatrix} \begin{bmatrix}1 & 3 \\0 & 2 \end{bmatrix}$$ is not possible