/*! 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 54 Is it possible for \(a 2 \times ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 54

Is it possible for \(a 2 \times 3\) matrix to equal a \(3 \times 2\) matrix? Explain.

Short Answer

Expert verified
In conclusion, it is not possible for a \(2 \times 3\) matrix to be equal to a \(3 \times 2\) matrix as they have different dimensions (2 rows and 3 columns vs. 3 rows and 2 columns). Two matrices can only be considered equal if they have the same dimensions and corresponding elements are equal.

Step by step solution

01

Understand the dimensions of the matrices given

The given dimensions in the exercise are a 2x3 matrix and a 3x2 matrix. A 2x3 matrix has 2 rows and 3 columns, while a 3x2 matrix has 3 rows and 2 columns. Here's an example of each: 2x3 matrix: \[ \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \] 3x2 matrix: \[ \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \\ b_{31} & b_{32} \end{bmatrix} \]
02

Determine when two matrices can be considered equal

Two matrices can be considered equal if and only if they meet the following conditions: 1. Both matrices have the same dimensions (the same number of rows and columns). 2. The corresponding elements in both matrices are equal, i.e. \(a_{ij} = b_{ij}\) for all i and j.
03

Check if the given matrices meet the conditions for equality

For the 2x3 matrix and the 3x2 matrix given in the exercise, they do not fulfill the first condition for equality. The 2x3 matrix has 2 rows and 3 columns, while the 3x2 matrix has 3 rows and 2 columns. Since their dimensions are different, it is impossible for these matrices to be equal. So, in conclusion, it is not possible for a \(2 \times 3\) matrix to be equal to a \(3 \times 2\) matrix.

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

Evaluate the given expression. Take \(A=\left[\begin{array}{rrr}1 & -1 & 0 \\\ 0 & 2 & -1\end{array}\right], B=\left[\begin{array}{rrr}3 & 0 & -1 \\ 5 & -1 & 1\end{array}\right]\), and \(C=\left[\begin{array}{lll}x & 1 & w \\ z & r & 4\end{array}\right] .\) $$ 3 B^{T} $$

Reduce the payoff matrices by dominance. $$ \begin{array}{rrrr} & & \mathbf{B} & \\ & a & b & c \\ p & {\left[\begin{array}{rrr} 1 & -1 & -5 \\ q & 4 & 0 & 2 \\ \mathbf{A} & r & 3 & -3 & 10 \\ 3 & -5 & -4 \end{array}\right]} \end{array} $$

Find: (a) the optimal mixed row strategy; (b) the optimal mixed column strategy, and (c) the expected value of the game in the event that each player uses his or her optimal mixed strategy. $$ P=\left[\begin{array}{rr} -1 & 0 \\ 1 & -1 \end{array}\right] $$

If \(A\) and \(B\) are \(2 \times 3\) matrices and \(A=B\), what can you say about \(A-B ?\) Explain.

Decide whether the game is strictly determined. If it is, give the players'optimal pure strategies and the value of the game. $$ \begin{gathered} \text { B } \\ p & q \\ \text { A } \left.\begin{array}{rr} a \\ 1 & 1 \\ 2 & -4 \end{array}\right] \end{gathered} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.