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What are the dimensions of I?  What are the dimensions of ˜I? Which is correct: A>=B A<=B A>B A

What are the dimensions of I?  What are the dimensions of ˜I? Which is correct: A>=B A<=B A>B A

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

What are the dimensions of I? 

What are the dimensions of ˜I?

Which is correct:

A>=B

A<=B

A>B

A<B 

A = B

or There isn't enough information to say definitively.

Consider the following equation: \[ B = IA\tilde{I} \] where \( A \in \mathbb{R}^{3 \times 2} \) and \( I, \tilde{I} \) represent identity matrices. ### Explanation This equation represents a matrix multiplication where: - \( B \) is the resulting matrix. - \( A \) is a matrix with dimensions \( 3 \times 2 \), which means it has 3 rows and 2 columns. - \( I \) and \( \tilde{I} \) are identity matrices. An identity matrix is a square matrix with 1s on the diagonal and 0s elsewhere. The dimensions of these identity matrices will depend on the context of matrix multiplication with \( A \), maintaining the compatibility of the multiplication.
Transcribed Image Text:Consider the following equation: \[ B = IA\tilde{I} \] where \( A \in \mathbb{R}^{3 \times 2} \) and \( I, \tilde{I} \) represent identity matrices. ### Explanation This equation represents a matrix multiplication where: - \( B \) is the resulting matrix. - \( A \) is a matrix with dimensions \( 3 \times 2 \), which means it has 3 rows and 2 columns. - \( I \) and \( \tilde{I} \) are identity matrices. An identity matrix is a square matrix with 1s on the diagonal and 0s elsewhere. The dimensions of these identity matrices will depend on the context of matrix multiplication with \( A \), maintaining the compatibility of the multiplication.
Expert Solution
Step 1: Introduction

The multiplication of two matrices is defined if and only if the number of rows in the first matrix is equal to the number of columns in the second matrix.

Since, I comma space I with tilde on top represents identity matrices, they must be square matrices.

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