The number of additions and multiplications involved in performing Gaussian elimination on any m x n upper triangular ma...

Question

The number of additions and multiplications involved in performing Gaussian elimination on any m x n upper triangular matrix is of the order

A. O(n)
B. O(n^2)
C. O(n^3)
D. O(n^4)

Accepted Answer

The complexity is O(n^2), so the answer is B. Gaussian elimination converts a matrix to row echelon form by eliminating entries below each pivot. When the matrix is already upper triangular, no row operations are needed below the diagonal. The only work remaining is the back-substitution phase, which requires visiting each of the n rows and performing operations proportional to the row index, leading to O(n^2) total operations.

The number of additions and multiplications involved in performing Gaussian elimination on any m x n upper triangular matrix is of the order A. O(n) B. O(n^2) C. O(n^3) D. O(n^4)