Determine the type of the matrix
given by 57, zero, zero, zero, negative 72, zero, zero, zero, zero. Is it (A) a row matrix, (B) an
identity matrix, (C) a diagonal matrix, or (D) a column matrix?
Now, if we look carefully at these
definitions, we see that we can disregard two of them immediately. We know that a row matrix is just
as it sounds. It’s a matrix that consists of
exactly one row. Our matrix, of course, has three
rows, so it cannot be a row matrix. Similarly, a column matrix consists
of exactly one column. And our matrix has three. So the answer cannot be (D). And so we have two left to choose
from. We have the identity matrix and the
diagonal matrix. Both of these matrices are special
types of square matrices. We know that an identity matrix has
all elements equal to zero except those in the main or leading diagonal.
And in this case, those have to be
equal to one as shown. Then a diagonal matrix does look
quite similar. All the elements above and below
the main diagonal are equal to zero. And then we have a series of
nonzero elements that only occur in the main diagonal. Now, not all of those elements
needs to be nonzero. But we know that all of them can’t
be zero because then we would have a null or zero matrix. And so, by comparing these
definitions to our matrix, we see we can also disregard the identity matrix. We have 57 and negative 72. We can, however, say that all of
the elements that sit above the main diagonal, that’s this, are zero and the
elements that sit below it are zero. And so we have a diagonal
matrix. And the answer is (C).