Question

Define upper and lower triangular matris. If A=[[1,2,3],[-3,5,-1],[2,3,3]],B=[[1,7,4],[4,2,8],[3,8,4]],C=[[4,5,4],[3,3,2],[1,5,5]] then prove the A+(B+C)=(A+B)+C

Answer 1

An upper triangular matrix has all elements below the main diagonal as zero, while a lower triangular matrix has all elements above the main diagonal as zero. To prove A + (B + C) = (A + B) + C, perform the operations on the matrices and compare the results.

Step-by-step explanation:

An upper triangular matrix is a square matrix where all the elements below the main diagonal are zero. A lower triangular matrix is a square matrix where all the elements above the main diagonal are zero.

To prove that A + (B + C) = (A + B) + C, we can perform the operations on the matrices:

1. Add matrices B and C together
2. Add matrix A to the result obtained from step 1
3. This gives us the left-hand side of the equation
4. Add matrices A and B together
5. Add matrix C to the result obtained from step 4
6. This gives us the right-hand side of the equation
7. Compare the left-hand side and right-hand side to see if they are equal

By using this method, we can prove that A + (B + C) = (A + B) + C.