In Chapter 11, we will show that if no row interchanges are performed, an matrix can be factored into a product where is a lower triangular matrix with ones on its diagonal and is the upper...

In Chapter 11, we will show that if no row interchanges are performed, an

matrix can be factored into a product

where

is a lower triangular matrix with ones on its diagonal and

is the upper triangular matrix obtained from Gaussian elimination. For instance, if

Develop a function

that takes the factors

and

of a matrix

and computes det

Check your function by computing the determinant of the matrix

using ludet and MATLAB’s det.

The function lugauss in the software distribution computes the

decomposition of a matrix without using row exchanges. It must be the case that during row elimination, a zero never appears on the diagonal. Create three matrices, of dimension

and

and use ludet to compute the determinant of each matrix. Verify your results using det.