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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 10
Chapter 6, Problem 10

Use the given row transformation to change each matrix as indicated.
[156−4−12371],4×row 1 added to row 2\(\left\)[ \(\begin{matrix}\) 1 & 5 & 6 \\ -4 & -1 & 2 \\ 3 & 7 & 1 \(\end{matrix}\) \(\right\)], \(\quad\) 4 \(\times\) \(\text{row 1 added to row 2}\)

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1
Identify the given matrix and label its rows as \( R_1 \), \( R_2 \), and \( R_3 \).
Understand the row operation: "4 times row 1 added to row 2" means you will replace \( R_2 \) with \( R_2 + 4 \times R_1 \).
Write the new row 2 as \( R_2' = R_2 + 4R_1 \). This means you add 4 times each element of row 1 to the corresponding element of row 2.
Keep rows 1 and 3 unchanged, so \( R_1' = R_1 \) and \( R_3' = R_3 \).
Perform the addition element-wise for row 2 to get the updated matrix after the row transformation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Elementary Row Operations

Elementary row operations are basic manipulations performed on the rows of a matrix to simplify or solve systems of equations. These include swapping rows, multiplying a row by a nonzero scalar, and adding a multiple of one row to another. Understanding these operations is essential for matrix transformations and solving linear systems.
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Matrix Representation and Notation

A matrix is a rectangular array of numbers arranged in rows and columns. Each element is identified by its row and column position. Familiarity with matrix notation helps in accurately performing and describing operations like adding multiples of one row to another.
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Interval Notation

Row Addition Operation

The row addition operation involves adding a multiple of one row to another row to create zeros or simplify the matrix. For example, '4 times row 1 added to row 2' means multiplying every element in row 1 by 4 and adding the result to the corresponding elements in row 2, altering row 2 while keeping other rows unchanged.
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Related Practice
Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. x/(x2 + 4x - 5)

Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.

[8−2463]\(\left\)[ \(\begin{matrix}\) 8 & -2 & 4 & 6 & 3 \(\end{matrix}\) \(\right\)]

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix In.)

[5723]and[3−7−25]\(\left\)[ \(\begin{matrix}\) 5 & 7 \\ 2 & 3 \(\end{matrix}\) \(\right\)] \(\quad\) \(\text{and}\) \(\quad\) \(\left\)[ \(\begin{matrix}\) 3 & -7 \\ -2 & 5 \(\end{matrix}\) \(\right\)]

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Textbook Question

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x + 2)/((x + 2)(2x - 1))

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