FULLY SOLVE AND MAKE ANSWER CLEAR TO READ!!! ### Vector Span and Systems of Equations#### Problem StatementLet \( \mathbf{u} = \begin{bmatrix}16 \\-1\end{bmatrix} \) and \( \mathbf{v} = \begin{bmatrix}16 \\1\end{bmatrix} \). Show that \( \begin{bmatrix}h \\y\end{bmatrix} \) is in Span \(\{\mathbf{u}, \mathbf{v}\}\) for all \( h \) and \( y \).---#### Conceptual Question**How can it be shown that a vector \( \mathbf{b} \) is in Span \(\{\mathbf{u}, \mathbf{v}\}\)?**- **A.** Determine if the system containing \(\mathbf{u}, \mathbf{v}\), and \(\mathbf{b}\) is consistent. If the system is consistent, then \(\mathbf{b}\) is in Span \(\{\mathbf{u}, \mathbf{v}\}\).- **B.** Determine if the system containing \(\mathbf{u}, \mathbf{v}\), and \(\mathbf{b}\) is consistent. If the system is consistent, \(\mathbf{b}\) might be in Span \(\{\mathbf{u}, \mathbf{v}\}\).- **C.** Determine if the system containing \(\mathbf{u}, \mathbf{v}\), and \(\mathbf{b}\) is consistent. If the system is consistent, then \(\mathbf{b}\) is not in Span \(\{\mathbf{u}, \mathbf{v}\}\).- **D.** Determine if the system containing \(\mathbf{u}, \mathbf{v}\), and \(\mathbf{b}\) is consistent. If the system is inconsistent, then \(\mathbf{b}\) is in Span \(\{\mathbf{u}, \mathbf{v}\}\).---**Let \(\mathbf{b} = \begin{bmatrix}h \\y\end{bmatrix}\). Find the augmented matrix \([ \mathbf{u} \ \mathbf{v} \ \mathbf{b} ]\).**\[ \boxed{}\]---**How is a system determined as consistent?**- **A.** A system is consistent if there The system is \(\boxed{consistent}\) for all values of \(h\) and \(y\). So it can be stated that \(\begin{pmatrix}h \\y\end{pmatrix}\) is in Span \(\{u, v\}\) for all values of \(h\) and \(y\).

Given that Suppose that b=Let b Thus, the system containing u,v,b is consistent then b.Thus,…

Let u = 16 -1 Let b= and v= [C] 16 1 Show that How can it be shown that a vector b is in Span {u, v}? 16 16 h -1 1 y y O A. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span (u, v). OB. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span (u, v). OC. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is not in Span (u, v). O D. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then b is in Span (u, v). is in Span (u, v) for all h and y. Find the augmented matrix u v b b]. How is a system determined as consistent? OA. A system is consistent if there are no solutions. B. A system is consistent only if all of the variables equal each other. OC. A system is consistent if there is one solution or infinitely many solutions. OD. Solve for the variables after setting the equations equal to 0. Row reduce the augmented matrix to its reduced echelon form.

Let u = 16 -1 Let b= and v= [C] 16 1 Show that How can it be shown that a vector b is in Span {u, v}? 16 16 h -1 1 y y O A. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span (u, v). OB. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span (u, v). OC. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is not in Span (u, v). O D. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then b is in Span (u, v). is in Span (u, v) for all h and y. Find the augmented matrix u v b b]. How is a system determined as consistent? OA. A system is consistent if there are no solutions. B. A system is consistent only if all of the variables equal each other. OC. A system is consistent if there is one solution or infinitely many solutions. OD. Solve for the variables after setting the equations equal to 0. Row reduce the augmented matrix to its reduced echelon form.

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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