/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 59 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 59

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Matrix row operations remind me of what I did when solving a linear system by the addition method, although I no longer write the variables.

Short Answer

Expert verified
The statement makes sense. Matrix row operations are indeed reminiscent of solving linear systems such as the addition method. In both cases, we are transforming the equations/system to a simpler form. The key difference is that while variables are explicit in the addition method, they are implicit in matrix row operations.

Step by step solution

01

Understand matrix row operations and the addition method for linear systems

Matrix row operations are a tool for making transformations to a matrix for it to reach a form that may be easier to work with. The three types of operations are Swapping two rows, Multiplying a row by a non-zero constant and Adding a row to another. The addition method for solving linear systems involves adding the equations to eliminate one of the variables, simplifying the system to a single variable.
02

Identify the similarities between the two operations

Both matrix row operations and the addition method for solving linear systems involve transforming equations to simplify their structure. In particular, the operation of adding one row to another in matrix operations is quite similar to adding two equations in the addition method for linear systems. When we do this operation on a matrix, it's just like simultaneously performing the addition on the corresponding equations.
03

Identify the key difference

The key difference between the two methods is in the presentation of the systems. The addition method retains the variables within the systems during solving, while matrix row operations deal purely with the coefficients and constants - the variables are 'understood' to be there but aren't actively written out.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the following matrices: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) $$ A=\left[\begin{array}{r} {2} \\ {-4} \\ {1} \end{array}\right], \quad B=\left[\begin{array}{r} {-5} \\ {3} \\ {-1} \end{array}\right] $$

Will help you prepare for the material covered in the next section. Multiply: $$ \left[\begin{array}{ll} {a_{11}} & {a_{12}} \\ {a_{21}} & {a_{22}} \end{array}\right]\left[\begin{array}{ll} {1} & {0} \\ {0} & {1} \end{array}\right] $$ After performing the multiplication, describe what happens to the elements in the first matrix.

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{rrr} {1} & {-1} & {1} \\ {5} & {0} & {-2} \\ {3} & {-2} & {2} \end{array}\right], \quad B=\left[\begin{array}{rrr} {1} & {1} & {0} \\ {1} & {-4} & {5} \\ {3} & {-1} & {2} \end{array}\right] $$

Let $$ A=\left[\begin{array}{rr} {-3} & {-7} \\ {2} & {-9} \\ {5} & {0} \end{array}\right] \text { and } B=\left[\begin{array}{rr} {-5} & {-1} \\ {0} & {0} \\ {3} & {-4} \end{array}\right] $$ Solve each matrix equation for X. $$ X-A=B $$

The figure shows the letter \(L\) in a rectangular coordinate system. The figure can be represented by the matrix $$ B=\left[\begin{array}{llllll} {0} & {3} & {3} & {1} & {1} & {0} \\ {0} & {0} & {1} & {1} & {5} & {5} \end{array}\right] $$ Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0,5), to the starting point, (0,0) . Use these ideas to solve Exercises 53-60. a. If \(A=\left[\begin{array}{rr}{1} & {0} \\ {0} & {-1}\end{array}\right],\) find \(A B\). b. Graph the object represented by matrix \(A B .\) What effect does the matrix multiplication have on the letter \(L\) represented by matrix \(B ?\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.