Q38E Find the QR factorization of A=[... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 5: Q38E (page 225)

Find the QR factorization of $A = [\begin{matrix} 0 & - 3 & 0 \\ 0 & 0 & 0 \\ 2 & 0 & 0 \\ 0 & 0 & 4 \end{matrix}]$ .

Short Answer

Expert verified

The solution is $QR = [\begin{matrix} 0 & - 1 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{matrix}]$ .

Step by step solution

`Explanation of the solution

Consider the matrix A as follows.

$A = [\begin{matrix} 0 & - 3 & 0 \\ 0 & 0 & 0 \\ 2 & 0 & 0 \\ 0 & 0 & 4 \end{matrix}]$

The vectors are orthogonal.

role="math" localid="1660103522754" ${\overset{鈬赌}{V}}_{1} = 2 {\overset{鈬赌}{e}}_{3} {\overset{鈬赌}{V}}_{2} = - 3 {\overset{鈬赌}{e}}_{1} {\overset{鈬赌}{V}}_{3} = 4 {\overset{鈬赌}{e}}_{4} Q = [\begin{matrix} \frac{{\overset{鈬赌}{V}}_{1}}{||{\overset{鈬赌}{V}}_{1}||} & \frac{{\overset{鈬赌}{V}}_{2}}{||{\overset{鈬赌}{V}}_{2}||} \end{matrix}] \begin{matrix} \frac{{\overset{鈬赌}{V}}_{3}}{||{\overset{鈬赌}{V}}_{3}||} = [\begin{matrix} 0 & - 1 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}] \end{matrix} R = [\begin{matrix} ||{\overset{鈬赌}{V}}_{1}|| & 0 & 0 \\ 0 & ||{\overset{鈬赌}{V}}_{2}|| & 0 \\ 0 & 0 & ||{\overset{鈬赌}{V}}_{3}|| \end{matrix}] R = [\begin{matrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{matrix}] Thus, the QR factorization is QR = [\begin{matrix} 0 & - 1 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{matrix}] .$

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91影视

Find the QR factorization of $A = [\begin{matrix} 0 & - 3 & 0 \\ 0 & 0 & 0 \\ 2 & 0 & 0 \\ 0 & 0 & 4 \end{matrix}]$ .

Short Answer

Step by step solution

`Explanation of the solution

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91影视

Find the QR factorization of A=[0-30000200004].

Short Answer

Step by step solution

`Explanation of the solution

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Find the QR factorization of $A = [\begin{matrix} 0 & - 3 & 0 \\ 0 & 0 & 0 \\ 2 & 0 & 0 \\ 0 & 0 & 4 \end{matrix}]$ .