Video Transcript
Given that 𝑂 is the zero matrix of
order one by three, find 𝑂 minus the one-by-three matrix one, two, three.
In this question, we’re told the 𝑂
is the zero matrix of order one by three. We need to use this to determine
the value of 𝑂 minus the one-by-three matrix one, two, three. To do this, let’s start by
recalling what we mean by a zero matrix. We recall we call a matrix a zero
matrix if every single entry in our matrix is equal to zero. So every entry in matrix 𝑂 is
equal to zero. Next, we’re also told the order of
matrix 𝑂 is one by three. And remember, the order of a matrix
is the number of rows by the number of columns. So our matrix 𝑂 has one row and
three columns. And all of its entries are equal to
zero. So 𝑂 is the one-by-three matrix
zero, zero, zero.
We can now use this to help us
evaluate the matrix expression we’re given. By substituting 𝑂 by the
one-by-three matrix zero, zero, zero into our matrix expression, we get 𝑂 minus the
one-by-three matrix one, two, three is equal to this. So all we need to do is subtract
these two matrices. To do this, we’re going to first
need to recall what we mean when we’re subtracting two matrices.
We need to know that to subtract
two matrices of the same order, we just subtract the corresponding entries. So we’re first going to need to
check that our matrices are the same order. Remember, this means checking that
they have the same number of rows and columns. Our first matrix, matrix 𝑂, is a
one-by-three matrix. It has one row and three
columns. And our second matrix also has only
one row and three columns. So they are in fact of the same
order. This means to subtract them, we
just subtract the corresponding entries.
So to find the entry in row one,
column one of our matrix, we need to subtract the entries in row one, column one of
our two matrices. This will give us zero minus
one. To find the entry in row one,
column two of our matrix, we need to subtract the entries in row one, column two of
our two matrices. This gives us zero minus two. Finally, we’ll do the same to find
the entry in row one, column three. We subtract the entries in row one,
column three of our two matrices. This gives us zero minus three. And now we can just calculate these
three expressions. We get the one-by-three matrix
negative one, negative two, negative three, which is our final answer.
Therefore, given that 𝑂 is the
zero matrix of order one by three, we were able to show that 𝑂 minus the
one-by-three matrix one, two, three is equal to the one-by-three matrix negative
one, negative two, negative three.
