Question

An upper triangular matric is square matrix with all zeros below its daignal. A lower triangular matrix is a square matrix with all zeros above its diagonal. (a)for all 3×3 upper triangular matirices U, verify that U2 is also upper triangular

Answer 1

U₂₁ and U₂₂ fits in the line of upper triangular

Explanation:

As explain in the question

An upper triangular matric is square matrix with all zeros below its daignal. A lower triangular matrix is a square matrix with all zeros above its diagonal.

(as shown in the attached image)

(a)for all 3×3 upper triangular matirices U, verify that U2 is also upper triangular

for a matrices U (having a 3*3 matrix), assuming for example, U is given below:

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

the element in the upper triangular are 1,2,3,5,6,9 (U₁₁, U₁₂, U₁₃; , U₂₂, U₂₃, U₂₂)

while lower triangular are 0,0,0, the element in the lower triangular are (U₂₁, U₃₁,U₃₂)

U₂₁ and U₂₂ fits in the line of upper triangular