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x Y +8 -2x - 7y - 3z = 16. +t

x Y +8 -2x - 7y - 3z = 16. +t

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The image depicts a system of linear equations and how it can be represented in vector notation. The equation given is: \[ -2x - 7y - 3z = 16. \] Accompanying this equation is a vector representation of the system of equations, indicating a combination of vectors with scalar multiples. The vector representation is structured as follows: \[ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} \text{[blank]} \\ \text{[blank]} \\ \text{[blank]} \end{bmatrix} + s \begin{bmatrix} \text{[blank]} \\ \text{[blank]} \\ \text{[blank]} \end{bmatrix} + t \begin{bmatrix} \text{[blank]} \\ \text{[blank]} \\ \text{[blank]} \end{bmatrix} \] In this notation: - \( x \), \( y \), \( z \) are variables representing coordinates or scalar quantities in a vector. - The blanks in each vector indicate the coefficients or values that need to be determined or added to make up the vectors. - \( s \) and \( t \) are scalar multiples that scale the corresponding vectors in the linear combination. This representation is useful for understanding systems of equations in terms of vector spaces and linear algebra, providing a more geometric interpretation of solutions to the equations.
Transcribed Image Text:The image depicts a system of linear equations and how it can be represented in vector notation. The equation given is: \[ -2x - 7y - 3z = 16. \] Accompanying this equation is a vector representation of the system of equations, indicating a combination of vectors with scalar multiples. The vector representation is structured as follows: \[ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} \text{[blank]} \\ \text{[blank]} \\ \text{[blank]} \end{bmatrix} + s \begin{bmatrix} \text{[blank]} \\ \text{[blank]} \\ \text{[blank]} \end{bmatrix} + t \begin{bmatrix} \text{[blank]} \\ \text{[blank]} \\ \text{[blank]} \end{bmatrix} \] In this notation: - \( x \), \( y \), \( z \) are variables representing coordinates or scalar quantities in a vector. - The blanks in each vector indicate the coefficients or values that need to be determined or added to make up the vectors. - \( s \) and \( t \) are scalar multiples that scale the corresponding vectors in the linear combination. This representation is useful for understanding systems of equations in terms of vector spaces and linear algebra, providing a more geometric interpretation of solutions to the equations.
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