Find values of z so that u is in the set M To solve the problem, we need to find the value of \( z \) such that the vector \[\mathbf{u} = \begin{bmatrix} -8 \\ z \\ 12 \\ -6 \end{bmatrix}\]is in the set given by the span of the vectors\[M = \text{span} \left\{ \begin{bmatrix} -4 \\ 1 \\ 2 \\ 3 \end{bmatrix}, \begin{bmatrix} 0 \\ -4 \\ 2 \\ -5 \end{bmatrix}, \begin{bmatrix} 0 \\ 0 \\ -4 \\ 2 \end{bmatrix} \right\}.\]This means that the vector \(\mathbf{u}\) can be expressed as a linear combination of the vectors in the set \(M\). We need to determine the coefficients for each of the vectors in \(M\) such that when combined, they equal \(\mathbf{u}\).The task is to solve for \(z\) and express \(\mathbf{u}\) as:\[a \begin{bmatrix} -4 \\ 1 \\ 2 \\ 3 \end{bmatrix} + b \begin{bmatrix} 0 \\ -4 \\ 2 \\ -5 \end{bmatrix} + c \begin{bmatrix} 0 \\ 0 \\ -4 \\ 2 \end{bmatrix}=\begin{bmatrix} -8 \\ z \\ 12 \\ -6 \end{bmatrix}.\]Enter the value of \( z \) in the box provided:\( z = \) \(\boxed{}\)

Answered: Find the value of z so that -8' 1 -4 is…

Find the value of z so that -8' 1 -4 is in the set M= span 12 2 2 Enter the value below:

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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