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
ANSWERED
asked 2021-06-06
Using givens rotation during QU factorization of the matrix A below, Make element (3,1) in A zero.
\([A]=\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 2 & 6 & 9\end{bmatrix}\)

Answers (1)

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.

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