Video: Determining Whether the Matrix Is Square, Column, Unit, or Row Matrix

Determine the type of the matrix −8, 2 and −7, −1. [A] Column matrix [B] Row matrix [C] Square matrix [D] Unit matrix.

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Video Transcript

Determine the type of the matrix negative eight, two, negative seven, negative one. Is it a column matrix, a row matrix, a square matrix, or a unit matrix?

Let’s consider what each of these different types of matrices are in turn, beginning with a column matrix. A column matrix is a matrix of order 𝑚 by one. It can have any number of rows 𝑚, but only one column. The matrix in this question has two columns. And therefore it isn’t a column matrix.

Next, let’s consider whether it could be a row matrix. A row matrix is a matrix of order one by 𝑛. It can have any number of columns 𝑛. But it only has one single row. This matrix has two rows. And therefore it isn’t a row matrix.

What about a square matrix? A square matrix is a matrix of order 𝑛 by 𝑛. It has the same number of rows and columns. This matrix has two rows and two columns. It’s of order two by two. Therefore, the matrix in this question is a square matrix.

Could it also be a unit matrix? A unit matrix is a special type of square matrix in which the elements on the leading diagonal are always equal to one and all of the other elements in the matrix are equal to zero. If we look at our matrix, we can see that this isn’t the case. The elements are negative eight, two, negative seven, and negative one. Therefore, the type of the matrix negative eight, two, negative seven, negative one is a square matrix.

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