/*! 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 13 Concept Check Find the dimension... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 13

Concept Check Find the dimension of each matrix. Identify any square, column, or row matrices. $$\left[\begin{array}{rr} -4 & 8 \\ 2 & 3 \end{array}\right]$$

Short Answer

Expert verified
The dimension is 2脳2. It is a square matrix.

Step by step solution

01

- Identify the Number of Rows

Count the number of horizontal lines of elements (rows). This matrix has 2 rows.
02

- Identify the Number of Columns

Count the number of vertical lines of elements (columns). This matrix has 2 columns.
03

- Determine the Dimension

Combine the number of rows and columns to find the dimension. The dimension of the matrix is given as rows 脳 columns. So, this matrix is 2脳2.
04

- Identify Matrix Type

A square matrix has the same number of rows and columns. Since this matrix is 2脳2, it is square. It is not strictly a row or column matrix because it has more than one row and one column.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

matrix types
Matrices come in different types based on their dimensions and the arrangement of their elements. Understanding these types is fundamental in linear algebra. Here are the main types of matrices you will encounter:
  • Row Matrix: A matrix with only one row.
  • Column Matrix: A matrix with only one column.
  • Square Matrix: A matrix with the same number of rows and columns.
  • Rectangular Matrix: A matrix with different numbers of rows and columns.
Recognizing these types helps in determining the appropriate operations and solutions for different mathematical problems.
row matrix
A row matrix is a matrix that consists of a single row of elements. It鈥檚 a special type of matrix where the number of rows is 1, and the number of columns can be any positive integer. For instance, the following matrix is a row matrix: \[ \left[\begin{array}{ccc} 4 & -5 & 3 \end{array}\right] \] Here, you can see there is just one row and three columns. This kind of matrix is particularly useful when you are working with vectors in linear algebra, representing data points, or performing operations like addition, subtraction, and multiplication involving row vectors.
column matrix
A column matrix features only one column of elements. This means the matrix has just one column but can have multiple rows. For example: \[ \left[\begin{array}{r} 7 \ -2 \ 5 \end{array}\right] \] This matrix has three rows and one column, making it a column matrix. Column matrices are frequently used to represent vectors. They are helpful in various computations and transformations in linear algebra and other fields requiring matrix operations. Each element in a column matrix can be seen as an entry in a vector.
square matrix
A square matrix has an equal number of rows and columns. This symmetry makes square matrices exceptionally important in many areas of mathematics, particularly in solving systems of linear equations and in performing operations like finding determinants or eigenvalues. An example of a square matrix is: \[ \left[\begin{array}{rr} -4 & 8 \ 2 & 3 \end{array}\right] \] This matrix is 2脳2, meaning it has 2 rows and 2 columns. Square matrices can be of any size (n脳n), and their properties make them particularly useful in advanced mathematical computations and theoretical work.

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

Solve each problem. A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for \(\$ 6.00\) per gallon. She wishes to mix three grades of water selling for \(\$ 9.00, \$ 3.00,\) and \(\$ 4.50\) per gallon, respectively. She must use twice as much of the S4.50 water as of the \(\$ 3.00\) water. How many gallons of each should she use?

Use Cramer's rule to solve each system of equations. If \(D=0,\) use another method to determine the solution set. $$\begin{array}{r} 4 x+3 y=9 \\ 12 x+9 y=27 \end{array}$$

Use Cramer's rule to solve each system of equations. If \(D=0,\) use another method to determine the solution set. $$\begin{aligned} x+2 y+3 z &=4 \\ 4 x+3 y+2 z &=1 \\ -x-2 y-3 z &=0 \end{aligned}$$

Supply and Demand In many applications of economics, as the price of an item goes up, demand for the item goes down and supply of the item goes up. The price where supply and demand are equal is the equilibrium price, and the resulting sup. ply or demand is the equilibrium supply or equilibrium demand. Suppose the supply of a product is related to its price by the equation $$p=\frac{2}{3} q$$ where \(p\) is in dollars and \(q\) is supply in appropriate units. (Here, \(q\) stands for quantity.) Furthermore, suppose demand and price for the same product are related by $$p=-\frac{1}{3} q+18$$ where \(p\) is price and \(q\) is demand. The system formed by these two equations has solution \((18,12),\) as seen in the graph. (GRAPH CANNOT COPY) Suppose the demand and price for a certain model of electric can opener are related by \(p=16-\frac{5}{4} q\), where \(p\) is price, in dollars, and \(q\) is demand, in appropriate units. Find the price when the demand is at each level. (a) 0 units (b) 4 units (c) 8 units

Summers wins \(200,000\) in the Louisiana state lottery. He invests part of the money in real estate with an annual return of \(3 \%\) and another part in a money market account at \(2.5 \%\) interest. He invests the rest, which amounts to \(80,000\) less than the sum of the other two parts, in certificates of deposit that pay \(1.5 \% .\) If the total annual interest on the money is \(4900,\) how much was invested at each rate?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.