Video: Identifying a Column Matrix

Determine which of the following matrices is a column matrix. [A] [2, βˆ’2 and 3, 5] [B] [2 and βˆ’2 and 3] [C] [2, 0 and 0, 5] [D] [0, 0 and 0, 0] [E] [2, βˆ’2, 3]

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Video Transcript

Determine which of the following matrices is a column matrix. Is it (A) two, negative two, three, five? (B) Two, negative two, three. Is it (C) two, zero, zero, five? Is it (D) zero, zero, zero, zero? Or is it (E) two, negative two, three?

Let’s remind ourselves what we mean when we say that a matrix is a column matrix. We say that an π‘š by 𝑛 matrix or a matrix order π‘š by 𝑛 has π‘š rows and 𝑛 columns. Now, if 𝑛 is equal to one, we call this a column matrix. In other words, if the matrix only has one column, it’s a column matrix. So let’s find the order of each of our individual matrices. Matrix 𝐴 has two rows and two columns, so it’s a two-by-two matrix. Matrix 𝐡 has three rows and one column, so it’s a three by one. Matrix 𝐢 is again a two by two, as is matrix 𝐷. And then we have the matrix 𝐸, which has one row and three columns. So that’s one by three. Now, if we look carefully and we compare each of these to our definition, we see that the matrix which has a value of 𝑛 equal to one is the matrix 𝐡. And so the matrix which is a column matrix is indeed 𝐡.

Now, in fact, we’re also able to name the other types of matrices. When π‘š is equal to 𝑛, in other words, when the number of rows is equal to the number of columns, we say the matrix is square. So matrix 𝐴 is square, as is matrix 𝐢. Now, matrix 𝐷 is also square, but this is a special type of matrix in itself. Every single element in this matrix is zero. And when we have a square matrix where this is the case, we call this a null matrix or zero matrix. And then, finally, let’s consider the matrix 𝐸. This time, the value of π‘š is equal to one. There is simply one row, and so we call this a row matrix.

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