2. Write $\vec{v} = \begin{bmatrix} 5 \\ 3 \\ -11 \\ 11 \\ 9 \end{bmatrix}$ as a linear combination of $\begin{bmatrix} 1 \\ 2 \\ -3 \\ 4 \\ -1 \end{bmatrix}$, $\begin{bmatrix} 1 \\ 2 \\ 0 \\ 2 \\ 1 \end{bmatrix}$, $\begin{bmatrix} 0 \\ 1 \\ 1 \\ 1 \\ -4 \end{bmatrix}$, $\begin{bmatrix} 2 \\ 1 \\ -1 \\ 2 \\ 1 \end{bmatrix}$, $\begin{bmatrix} 0 \\ 2 \\ 2 \\ -1 \\ -1 \end{bmatrix}$. Is the solution unique?

Answered: 2 i İ2 Write i =-11 as a linear…

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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Question

2. Write $\vec{v} = \begin{bmatrix} 5 \\ 3 \\ -11 \\ 11 \\ 9 \end{bmatrix}$ as a linear combination of $\begin{bmatrix} 1 \\ 2 \\ -3 \\ 4 \\ -1 \end{bmatrix}$, $\begin{bmatrix} 1 \\ 2 \\ 0 \\ 2 \\ 1 \end{bmatrix}$, $\begin{bmatrix} 0 \\ 1 \\ 1 \\ 1 \\ -4 \end{bmatrix}$, $\begin{bmatrix} 2 \\ 1 \\ -1 \\ 2 \\ 1 \end{bmatrix}$, $\begin{bmatrix} 0 \\ 2 \\ 2 \\ -1 \\ -1 \end{bmatrix}$. Is the solution unique?

Expert Solution

Step 1

The inverse of the matrix: $A^{- 1}$ is that the inverse of Matrix for a matrix A. a simple formula are typically accustomed to calculate the inverse of a two matrix. to boot, we have a tendency to should recognize the determinant and adjoint of a three matrix therefore on cipher its inverse. The inverse of a matrix is another matrix that yields the increasing identity once increased with the provided matrix.