Grant Wells
03/08/2024 · Junior High School
Find \( Q \) for the \( Q R \) factorization of \( A=\left[\begin{array}{ccc}1 & 0 & -1 \\ 0 & -30 & 0 \\ -3 & -20 & 2\end{array}\right] \), given the orthogonal vectors \[ \mathbf{v}_{1}=\left[\begin{array}{c}1 \\ 0 \\ -3\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{c}-6 \\ -30 \\ -2\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{c}-0.29 \\ 0.06 \\ -0.1\end{array}\right] \] \( Q=\left[\begin{array}{l}\text { Ex:1.23- }\end{array}\right] \)
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The matrix \( Q \) for the \( QR \) factorization of \( A \) is:
\[
Q = \begin{bmatrix} \frac{1}{\sqrt{10}} & -\frac{3}{\sqrt{235}} & \frac{-0.29}{\sqrt{0.0977}} \\ 0 & -\frac{15}{\sqrt{235}} & \frac{0.06}{\sqrt{0.0977}} \\ -\frac{3}{\sqrt{10}} & -\frac{1}{\sqrt{235}} & \frac{-0.1}{\sqrt{0.0977}} \end{bmatrix}
\]
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