Question Video: Determining the Type of Matrix Given Mathematics

Video Transcript

If the matrix 𝐴 is equal to five, five, zero, which of the following is true? Is it (A) the matrix 𝐴 is a unit matrix? (B) The matrix 𝐴 is a diagonal matrix. (C) The matrix 𝐴 is a square matrix. (D) The matrix 𝐴 is a column matrix. Or (E) the matrix 𝐴 is a row matrix.

We recall that a matrix of order 𝑚 by 𝑛 has 𝑚 rows and 𝑛 columns. And if 𝑚 is equal to 𝑛 — in other words, the number of rows is equal to the number of columns — then the matrix is said to be square. So (C) is the square matrix. But we also know that both unit matrices and diagonal matrices must themselves be square. And so, let’s ask ourselves, is the matrix 𝐴 a square matrix? Well, it’s quite clear that it does not have the same number of rows and columns. In fact, it’s a one-by-three matrix. It has one row and three columns. And so since unit matrices and diagonal matrices are examples of square matrices, we’re able to disregard the first three options here. It cannot be any of these.

And so we’re left with two to choose from. We have column matrix and row matrix. Well, we know that a column matrix is such that 𝑛 is equal to one, we have one column, whereas a row matrix occurs when 𝑚 is equal to one, when there’s one row. Comparing the general form to the order of our matrix, and we can actually say that 𝑚 is equal to one and 𝑛 is equal to three. We have one row and three columns, so it cannot be a column matrix. But because 𝑚 is equal to one, it must be a row matrix.