Choose the description to match the correct matrix, triangular form

Question

Choose the description to match the correct matrix

triangular form

A  

B

C

D

E

Answer 1

The triangular matrix is choice D.

First, let's define a triangular matrix. A triangular matrix is a matrix where all values above OR below the main diagonal are equal to zero. In the case of an augmented matrix, ignore that column when determining which fits the rule.

Most obviously incorrect is choice C, as it doesn't have a main diagonal. C is just a column vector.

A and E are also incorrect as they don't have all zeros either above or below the diagonal.

B contains zeros both above AND below the diagonal. That type of matrix is just called a diagonal matrix. Since the diagonal is all 1s, the diagonal matrix is more specifically called an identity matrix. The augmented values actually represent the solutions to that system, in the form x=, y=, z=. All of that is to say B is not triangular.

That leaves D. One can see that below the diagonal (with values 1,1,1), there are all zeros. This fits the rule for triangular matrices, so it's the correct answer.