Given that 𝐴 equals to negative
seven, seven and 𝐵 equals to zero, negative five, find 𝐴𝐵 if possible.
You can multiply two matrices if
and only if the number of columns in the first matrix equals the number of rows in
the second. Otherwise, the product of two
matrices is undefined. Here matrix 𝐴 has one column and
matrix 𝐵 has one row. So we can multiply these
To find 𝐴𝐵 then, which is the
product of matrix 𝐴 and matrix 𝐵, we need to do the dot product. Let’s do this for the first row in
𝐴 and the first column in 𝐵. Negative seven multiply by zero is
zero. The first element in a matrix 𝐴𝐵
is therefore zero.
Then we multiply the elements in
our first row of 𝐴 by the second element in 𝐵. Negative seven multiplied by
negative five is 35. The element in the first row and
second column of the product of 𝐴𝐵 is therefore 35. Multiplying seven by zero gives us
The element in the first column and
the second row of our product is therefore zero. Finally, we multiply seven by
negative five to give us negative 35. And the final element of a product
𝐴𝐵 is negative 35. In this case then, 𝐴𝐵 is entirely
possible and its matrix is as shown.