## Description

1. Exercise 3.2.48.

2. Write your own Matlab code to compute QR factorization with:

Input: A matrix A ∈ R

m×n with m ≥ n.

Output: An orthorgonal matrix Q ∈ R

m×m and an upper triangular R ∈ R

m×n

such that

A = QR.

Look at iteration formula in (3.2.43). Test your code on matrices generated by randn(m,n)

in Matlab.

3. Exercise 3.3.10.

4. Write your own Matlab code to implement the Gram-Schmidt process with:

Input: A matrix A ∈ R

m×n with m ≥ n.

Output: An isometric matrix Q ∈ R

m×n and an upper triangular R ∈ R

n×n

, such that

A = QR and the diagonal entries of R are nonnegative.

Look at iteration formula in (3.4.19). Test your code on matrices generated by randn(m,n)

in Matlab.

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