Video Transcript
Given that 𝐴 is equal to negative three, negative seven, negative one, and three, four, one, and 𝐵 is equal to six, negative four, three, 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, we say that the product is undefined. Matrix 𝐴 has three columns and matrix 𝐵 has three rows. So we can indeed find the product 𝐴𝐵.
To do this then, we need to find the dot product of the rows and columns. This is where we multiply matching members and then add them together. First, we’re going to multiply the elements in the first row of 𝐴 by the elements of 𝐵. Negative three multiplied by six add negative seven multiplied by negative four add negative one times three is seven.
Then we’re going to multiply the elements in the second row of 𝐴 by the elements in 𝐵 and add them together. Three multiplied by six add four multiplied by negative four add one multiplied by three is five. The matrix 𝐴𝐵 is therefore given by seven, five.
