1.2 number 12 review ### Linear Algebra: Row Reduction and Solutions of Linear Systems#### Exercises 3 and 4**Objective:** Row reduce the matrices in Exercises 3 and 4 and convert them to reduced echelon form. Circle the pivot positions in the final matrix, and in the original matrix, and list the pivot columns.3.\[\begin{bmatrix}1 & 2 & 4 & 8 \\2 & 4 & 6 & 8 \\1 & 6 & 9 & 12 \\\end{bmatrix}\]4.\[\begin{bmatrix}1 & 2 & 4 & 5 \\2 & 4 & 5 & 4 \\4 & 5 & 4 & 2 \\\end{bmatrix}\]#### Exercise 5**Objective:** Describe the possible echelon forms of a nonzero $2 \times 2$ matrix. Use the symbols $\ast$, $\diamond$, and 0, as in the first part of Example 1.#### Exercise 6**Objective:** Repeat Exercise 5 for a nonzero $3 \times 2$ matrix.#### Exercises 7-14**Objective:** Find the general solutions of the systems whose augmented matrices are given.7.\[\begin{bmatrix}1 & 3 & 4 & 7 \\3 & 9 & 7 & 6 \\\end{bmatrix}\]8.\[\begin{bmatrix}1 & -3 & 0 & 5 \\3 & 7 & 0 & 9 \\\end{bmatrix}\]9.\[\begin{bmatrix}1 & 1 & 3 & -2 \\1 & 2 & 5 & -4 \\\end{bmatrix}\]10.\[\begin{bmatrix}1 & 0 & 3 & 0 \\2 & -2 & 5 & 4 \\\end{bmatrix}\]11.\[\begin{bmatrix}3 & -2 & 4 & 0 \\6 & -4 & 8 & 0 \\\end{bmatrix}\]12.\[\begin{bmatrix}2 & 6

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Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.3: Matrix Approa To Solving Linear Systems

Problem 51PS

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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1.2 number 12 review

### Linear Algebra: Row Reduction and Solutions of Linear Systems

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

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

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

#### Exercise 5
**Objective:** Describe the possible echelon forms of a nonzero $2 \times 2$ matrix. Use the symbols $\ast$, $\diamond$, and 0, as in the first part of Example 1.

#### Exercise 6
**Objective:** Repeat Exercise 5 for a nonzero $3 \times 2$ matrix.

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

7.
\[
\begin{bmatrix}
1 & 3 & 4 & 7 \\
3 & 9 & 7 & 6 \\
\end{bmatrix}
\]

8.
\[
\begin{bmatrix}
1 & -3 & 0 & 5 \\
3 & 7 & 0 & 9 \\
\end{bmatrix}
\]

9.
\[
\begin{bmatrix}
1 & 1 & 3 & -2 \\
1 & 2 & 5 & -4 \\
\end{bmatrix}
\]

10.
\[
\begin{bmatrix}
1 & 0 & 3 & 0 \\
2 & -2 & 5 & 4 \\
\end{bmatrix}
\]

11.
\[
\begin{bmatrix}
3 & -2 & 4 & 0 \\
6 & -4 & 8 & 0 \\
\end{bmatrix}
\]

12.
\[
\begin{bmatrix}
2 & 6

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