§8.2, Exercise 1. The 3 x 3 matrix 1 A = -() 2 5 2 -1 1 3 1 6 has rank two. Let r1,12, r3 be the rows of A and c1, C2, C3 be the columns of A. Find all scalars a1, ɑ2, ɑ3 and B1, B2, B3 such that airı+ a2r2 +a3r3 Bịcı + B2c2 + B3C3 0.
§8.2, Exercise 1. The 3 x 3 matrix 1 A = -() 2 5 2 -1 1 3 1 6 has rank two. Let r1,12, r3 be the rows of A and c1, C2, C3 be the columns of A. Find all scalars a1, ɑ2, ɑ3 and B1, B2, B3 such that airı+ a2r2 +a3r3 Bịcı + B2c2 + B3C3 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 6**
**§8.2, Exercise 1.** The \(3 \times 3\) matrix
\[ A = \begin{pmatrix} 1 & 2 & 5 \\ 2 & -1 & 1 \\ 3 & 1 & 6 \end{pmatrix} \]
has rank two. Let \( r_1, r_2, r_3 \) be the rows of \( A \) and \( c_1, c_2, c_3 \) be the columns of \( A \). Find all scalars \( \alpha_1, \alpha_2, \alpha_3 \) and \( \beta_1, \beta_2, \beta_3 \) such that
\[
\alpha_1 r_1 + \alpha_2 r_2 + \alpha_3 r_3 = 0
\]
\[
\beta_1 c_1 + \beta_2 c_2 + \beta_3 c_3 = 0.
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Transcribed Image Text:**Problem 6**
**§8.2, Exercise 1.** The \(3 \times 3\) matrix
\[ A = \begin{pmatrix} 1 & 2 & 5 \\ 2 & -1 & 1 \\ 3 & 1 & 6 \end{pmatrix} \]
has rank two. Let \( r_1, r_2, r_3 \) be the rows of \( A \) and \( c_1, c_2, c_3 \) be the columns of \( A \). Find all scalars \( \alpha_1, \alpha_2, \alpha_3 \) and \( \beta_1, \beta_2, \beta_3 \) such that
\[
\alpha_1 r_1 + \alpha_2 r_2 + \alpha_3 r_3 = 0
\]
\[
\beta_1 c_1 + \beta_2 c_2 + \beta_3 c_3 = 0.
\]
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