Question Video: Finding the Product of Two Given Matrices Mathematics

Consider the matrices 𝐴 = [1, 2, −7] and 𝐵 = [−4 and 6 and −2]. Find 𝐴𝐵 if possible.

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Video Transcript

Consider the matrices 𝐴 is equal to one, two, negative seven and 𝐵 is equal to negative four, six, negative two. Find 𝐴𝐵 if possible.

We recall that matrix multiplication is defined if the number of columns in the first matrix is equal to the number of rows in the second matrix. For example, an 𝑚-by-𝑛 matrix multiplied by an 𝑛-by-𝑘 matrix is defined. The resulting matrix will have 𝑚 rows and 𝑘 columns.

In this question, matrix 𝐴 has order one by three, as there is one row and three columns. Matrix 𝐵 has order three by one, as there are three rows and one column. This is known as a column matrix.

The number of columns in matrix 𝐴 is equal to the number of rows in matrix 𝐵. Therefore, the matrix 𝐴𝐵 will be defined. The matrix 𝐴𝐵 will therefore have one element equal to one multiplied by negative four plus two multiplied by six plus negative seven multiplied by negative two. This simplifies to negative four plus 12 plus 14, which in turn is equal to 22. 𝐴𝐵 is a matrix with one element, the number 22.

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