Number 4 linear algebra ### CHAPTER 1: Linear Equations in Linear Algebra**2.** a. \[ \begin{bmatrix} 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix} \]b.\[ \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 1 & 1 \end{bmatrix} \]c.\[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]d.\[ \begin{bmatrix} 0 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \]**Row reduce the matrices in Exercises 3 and 4 to reduced echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.****3.**\[ \begin{bmatrix} 1 & 2 & 4 & 8 \\ 2 & 4 & 5 & 4 \\ 3 & 6 & 9 & 12 \end{bmatrix} \]**4.**\[ \begin{bmatrix} 1 & 2 & 4 & 5 \\ 2 & 4 & 5 & 4 \\ 4 & 2 & 5 & 6 \end{bmatrix} \]**5. Describe the possible echelon forms of a nonzero 2 x 2 matrix. Use the symbols *, and 0, as in the first part of Example 1.****6. Repeat Exercise 5 for a nonzero 3 x 2 matrix.****Find the general solutions of the systems whose augmented matrices are given in Exercises 7-14.****7.** \[ \begin{bmatrix} 1 & 3 & 4 \\ 3 & 9 & 7

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Answered: Row reduce the matrices in Exercises 3…

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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Number 4 linear algebra

### CHAPTER 1: Linear Equations in Linear Algebra

**2.**

a.
\[ \begin{bmatrix}
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix} \]

b.
\[ \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 \\
0 & 0 & 1 & 1
\end{bmatrix} \]

c.
\[ \begin{bmatrix}
1 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 0 \\
0 & 0 & 1
\end{bmatrix} \]

d.
\[ \begin{bmatrix}
0 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix} \]

**Row reduce the matrices in Exercises 3 and 4 to reduced echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.**

**3.**
\[ \begin{bmatrix}
1 & 2 & 4 & 8 \\
2 & 4 & 5 & 4 \\
3 & 6 & 9 & 12
\end{bmatrix} \]

**4.**
\[ \begin{bmatrix}
1 & 2 & 4 & 5 \\
2 & 4 & 5 & 4 \\
4 & 2 & 5 & 6
\end{bmatrix} \]

**5. Describe the possible echelon forms of a nonzero 2 x 2 matrix. Use the symbols *, and 0, as in the first part of Example 1.**

**6. Repeat Exercise 5 for a nonzero 3 x 2 matrix.**

**Find the general solutions of the systems whose augmented matrices are given in Exercises 7-14.**

**7.**
\[ \begin{bmatrix}
1 & 3 & 4 \\
3 & 9 & 7

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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