Question

Find a QR factorization of A. Answers should be in exact form (i.e., do not use a calculator to get a decimal approximation). $$A = \begin{bmatrix} 1 & 1 & -1 \\ 1 & 0 & -2 \\ 0 & 1 & 0 \\ 1 & 1 & -1 \end{bmatrix}$$ A = [(,,,),(,,,), (,,,)] Note: Since there are an infinite number of QR factorizations, you must enter both Q and R for the question to determine whether your answer is correct.

Name: find a qr factorization of a answers should be in exact form ie do not use a calculator to get a decimal approximation a beginbmatrix 1 1 1 1 0 2 0 1 0 1 1 1 endbmatrix a note since there ar 53352
Uploaded: 2023-04-26T10:02:01-08:00
Duration: 3 min 15 s
Channel: Madhur L
Description: find a qr factorization of a answers should be in exact form ie do not use a calculator to get a decimal approximation a beginbmatrix 1 1 1 1 0 2 0 1 0 1 1 1 endbmatrix a note since there ar 53352

          Find a QR factorization of A. Answers should be in exact form (i.e., do not use a calculator to get a
decimal approximation).
$$A = \begin{bmatrix} 1 & 1 & -1 \\ 1 & 0 & -2 \\ 0 & 1 & 0 \\ 1 & 1 & -1 \end{bmatrix}$$
A = [(,,,),(,,,), (,,,)]
Note: Since there are an infinite number of QR factorizations, you must enter both Q and R for
the question to determine whether your answer is correct.

find a qr factorization of a answers should be in exact form ie do not use a calculator to get a decimal approximation a beginbmatrix 1 1 1 1 0 2 0 1 0 1 1 1 endbmatrix a note since there ar 53352

Added by Samuel H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

04/26/2023

Step 1

We apply Gram-Schmidt process to find an orthogonal basis. $q_1 = a_1 = \begin{bmatrix} 1 \\ 1 \\ 0 \\ 1 \end{bmatrix}$. $q_2 = a_2 - \frac{a_2 \cdot q_1}{q_1 \cdot q_1} q_1 = \begin{bmatrix} 1 \\ 0 \\ 1 \\ 1 \end{bmatrix} - \frac{1+0+0+1}{1+1+0+1} \begin{bmatrix} Show more…

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Find a QR factorization of A. Answers should be in exact form (i.e., do not use a calculator to get a decimal approximation). $$A = \begin{bmatrix} 1 & 1 & -1 \\ 1 & 0 & -2 \\ 0 & 1 & 0 \\ 1 & 1 & -1 \end{bmatrix}$$ A = [(,,,),(,,,), (,,,)] Note: Since there are an infinite number of QR factorizations, you must enter both Q and R for the question to determine whether your answer is correct.