Question Video: Types of Matrices Mathematics

Determine the type of the matrix [57, 0, 0 and 0, −72, 0 and 0, 0, 0]. [A] Row matrix [B] Identity matrix [C] Diagonal matrix [D] Column matrix


Video Transcript

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).

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