Q47. - Algebra 2

Question

Determine whether each matrix product is defined. If so, state the dimensions of the product.

47. $A_{4\times 1}·B_{2\times 1}$

Step-by-Step Solution

Answer

Matrix product of given matrices is not defined.

Step 1 - Write condition for matrix product to be defined.

For two matrices $A$ and $B$, the product $A·B$ is defined when number of columns of matrix $A$ is equal to the number of rows of matrix $B$. 

Step 2 - Write dimensions of given matrices

Matrix $A$ has 4 rows and 1 column and matrix $B$ has 2 rows and 1 column.

Step 3 - Check multiplication is defined or not

As, number of columns of matrix $A$ is not equal to the number of rows of matrix $B$.

So multiplication is not defined.