CSC338: Tutorial 4
1. Assume that
1 4.75 −4 What are the values of ||b||1, ||b||2, ||b||∞, ||A||1, and ||A||∞?
1
4−21 3 A = −2 5 −2 b = −5
2. Consider the matrix A from the previous question. Bob thinks that in the decomposition P A = LU of the matrix A, that P = I, the identity function. That is, no row exchanges will be performed as part of partial pivoting. The reason he believes so is because in A, the largest element in each row and each column is already on the diagonal. Is Bob right? Why or why not?
3. Compute the P A = LU factorization of the below matrix using pivoting.
2 6 8 A=4 8 4
135