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 𝑚 by 𝑛 matrix or a
matrix order 𝑚 by 𝑛 has 𝑚 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 𝐵 has three rows and one
column, so it’s a three by one. Matrix 𝐶 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 𝐵. And so the matrix which is a column
matrix is indeed 𝐵.
Now, in fact, we’re also able to
name the other types of matrices. When 𝑚 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 𝐶. 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 𝑚 is equal
to one. There is simply one row, and so we
call this a row matrix.
