Question

A matrix A = [aij] is an upper triangular matrix if = _____.

a. It is a square matrix and aij = 0, i < j

b. It is a square matrix and aij = 0, i > j

c. It is not a square matrix and aij = 0, i > j

d. It is not a square matrix and aij = 0​

Answer 1

Answer:

aij=0, for i>j

A square matrix will be upper triangular matrix if all the elements of the lower triangle are zeros.

aij=0, i>0

Answer 2

A matrix A=[aij] is an upper triangular matrix if ' it is a square matrix and   aij = 0 for all i>j '

example:

$\left[\begin{array}{ccc}1&2&3\\0&5&6\\0&0&9\end{array}\right]$

in the above matrix all the elements below the diagonal elements are 'ZERO'. And the elements below the diagonal elements has the value of

'i > j'. And only a square matrix can be an upper or lower triangular matrix.

So, the correct option is 'b'

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