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1 3 9 2 0 3 -4 1 2 2 3 0 Let b = 3 and let A = 1 Is b in the range of the linear transformation 3 4 5 * → Ax? Why or Why not?

1 3 9 2 0 3 -4 1 2 2 3 0 Let b = 3 and let A = 1 Is b in the range of the linear transformation 3 4 5 * → Ax? Why or Why not?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 23E
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Let \(\vec{b} = \begin{bmatrix} -1 \\ 3 \\ -1 \\ 4 \end{bmatrix}\) and let \(A = \begin{bmatrix} 1 & 3 & 9 & 2 \\ 1 & 0 & 3 & -4 \\ 0 & 1 & 2 & 3 \\ -2 & 3 & 0 & 5 \end{bmatrix}\). Is \(\vec{b}\) in the range of the linear transformation \(\vec{x} \rightarrow A\vec{x}\)? Why or why not?
Transcribed Image Text:Let \(\vec{b} = \begin{bmatrix} -1 \\ 3 \\ -1 \\ 4 \end{bmatrix}\) and let \(A = \begin{bmatrix} 1 & 3 & 9 & 2 \\ 1 & 0 & 3 & -4 \\ 0 & 1 & 2 & 3 \\ -2 & 3 & 0 & 5 \end{bmatrix}\). Is \(\vec{b}\) in the range of the linear transformation \(\vec{x} \rightarrow A\vec{x}\)? Why or why not?
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