Question

# Using givens rotation during QU factorization of the matrix A below, Make element (3,1) in A zero. [A]=\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 2 & 6 & 9\end{bmatrix}

Polynomial factorization
Using givens rotation during QU factorization of the matrix A below, Make element (3,1) in A zero.
$$[A]=\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 2 & 6 & 9\end{bmatrix}$$

2021-06-07

Step 1
Given matrix is :
$$A=\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 2 & 6 & 9\end{bmatrix}$$
Element $$(3,1) = 2$$
Step 2
Now, applying the operation $$R_{3}^{\prime}=R_{3}-2R_{2}$$ on A,A becomes
$$\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 0 & -8 & -7\end{bmatrix}$$
This is the required form.